Start a new game (obviously) and choose the beginner difficulty. Trust me on that, even Beginner starts out hard as balls. but its more forgiving then the higher difficulties.

Next thing is where to put your first base. Get it central to a big mass of land. Central USA, Russia/Mongolia, Western end of Brazil or central Africa should do nicely.
You need to shoot the Ufos down and manage to salvage the Wreckage. You cant salvage anything if the UFO crashes into the Ocean, so thats why you should place them there.

Now that you have your first base, you should IMMEADEATELY start building a 2nd base on one of the spots you didnt pick. Equip it with a Hangar, Storage and Big Radar (build one in the main base as well. you need as much coverage of the planet as fast as possible). this should take almost all of January.

Your Main Base (first one) should be your main Point of Opreation, means Soldiers, Engeneering and R&D will all take place in there. All other bases will be Outposts, made to Search and Intercept UFOs. You may build some defenses there but Aliens dont really Attack bases until later in the game.

Back to the main base. Click on the Reasearch tab and start researching the Laser Weapons Technology. use ALL your Reasearchers, since it will speed up the Process. While we're at it, if the money is enough, buy more Scientists and build another Living Quarter. You want your technology maxed out as fast as possible.
go back to the Worl map screen and speed it up a little. press the 1 Day button (theres not much to do now anyways.)
If your research finishes, read more here. If you get an UFO sighting - see you in the next chapter.

Now, your Laser Weapons technology is finished. Where are them Big guns? Well, you have the Technology, now to put it into a useable shell. Start the reasearch on the Laser pistol and do the same as above. 1 day. By now you should get a UFO warning before the Pistol research finishes.
If not, your first monthly review may be a little bit worse then it should be. anyways, I'll finish this topic here since I dont want our "Lucky" guys who met an UFO before to miss anything.

So you met an UFO. Congratulations! now off to Battle.
click on "center UFO, time = 5sec" and click the UFO. Select intercept and select an Interceptor and we're off.
If the UFO is away a little further, increase the time steps to 5 or 30 mins. now one of two things may happen.
a) you catch up to the UFO
b) you Lose the UFO
c) the UFO lands (it becomes a green X)

in case of a) you get to the fighting screen. Select the Standard Attack (2 shots, medium distance icon) This will mean the Interceptor will quickly catch up to its max range and slowly decrease its distance until it reaches minimum distance for its secondary weapon)

now the UFO may either flee or you get it. if it flees you're back to the World map and the chase continues, if you get it you'l either shoot it down ("UFO crashed", very Likely) or destroy it ("UFO destroyed", unlikely and bad in a way. this will not leave a Wreck and potential materials will be lost)
now its time for ground combat. read more at c)

in case of b) select to fly to the last known position. The Interceptor has a small radar range by itself, so it has a slim, but possible chance to find the UFO again (or another one altogether) If you reach the waypoint and not find tthe UFO you can either return to base (you'll use less fuel that way and save some money nad have the Interceptor ready again faster.
You can also make it patrol until it runs out of fuel or set new waypoints where you believe the UFO to be (this is why you want Radar coverage as quick as possible) Chances are the UFO is lost if you lose it, tho.

in case of c) you can start ground combat. Select the Intercept tab from the menu and select the Skyranger. for your Target, select the UFO site (the green X if it landed or white X if it crashed) we will now begin ground combat.
more in the next chapter

well, not right now. and chances are they will kick your ass instead. you'll see why immeadeately

You'll get an Equipment screen and will immeadiately see why you're in for a hard time. Your soldiers are in their way to fight an unknown meanace wearing Jumpsuits. yes. Cloth Jumpsuits. good luck.

Since you dont really should have any alternative weapons by now, everyone has either a rifle or a pistol. and that one guy with a Heavy Gun. click OK and its time to roll out.

A soldier should be selected, time to look at the UI. you have 4 numbers there - green, brown , red and Purple

Green - your time Units (TUs). its a measurement of "time" your units can move. Take a turn as a 2 minute interval, the time units show how much you can do in those 2 minutes. this stat is influenced by equipment slots filled and weapons equippe. Weapons with a "Heavy" in their name will cost you a lot more time units then "rifles" or "pistols". in addition, every slot on your shoulders, legs, belt or backpack will lower this stat as well.

Brown - Energy . Energy is needed to move. take it as the soldiers Stamina. If you move uphill or through heavy terrain (like wheat fields) you'll lose more then if you move on plain floors.
this stat is part of the learning system. Spend energy and the stat will rise.

Red - Health this is where it counts. this is how much abuse your soldiers can take until they are out cold. forever. it may say something like 30 or so now, but believe me, that is nothing.
If your soldiers stand in smoke (grey dots in the air) your Life bar will fill with a grey bar. If the grey bar reaches the current HP of your soldier will fall unconcious. and has to be revived with a Medi Bag. if you click the rank-symbol of your soldier (by now that golden R) you can see more detailed stats. for this part only "deadly Wounds" is interesting. If your soldier gets hit he has a chance to recieve a wound. the value of those wounds will be deducted by your soldiers Health every turn. Medi bags can be used to cure those wounds, tho.
one other thing - If your soldiers get injured, even if they are healed to full health with Medi Bags, they have to be Hospitalized. if they get hurt really badly they have to stay for months. you wouldnt want that to happen.

Purple - Morale the will to fight and the sanity of your soldier in one stat. If soldiers see other soldiers get hit or even die the morale will decrease. Morale can be boosted with Medi Bags, but if they lose some, its already too late. mostly.
Morale will be checked at each turns start. if soldiers dont pass the morale check they snap for the turn. they are either frozen in terror (reduces TUs to 0 for the turn), start to panic (they drop or throw their weapon and run as far as Energy and TUs allow them to. or they snap, which makes them fire snapshots in random directions until they run out of ammo or TUs. anyways whatever happens, its bad.
now back to Battle

skip your first turn. Trust me on that. on the Start of Turn 1 everyone will have full TUs. If a unit has enough TUs to fire a snapshot during the enmies turn they will fire if they see an enemy move, so if you manage to slightly cross the Line of Sight they will fire at you. and those aliens semm to have a way better aim then your guys. Best material they can offer. Rookies and Jumpsuits... I stray off topic.
my personal experience was if I move a soldier out of the Skyrangerin turn 1 its Omaha Beach all over again in 7 out of 10 cases.

since every battle is different here are some pointers :
1. Allways move in groups, but dont bunch up. if you are alone without TUs and have an alien looking at you you know you dun goof'd. its allways good to have some backup.
2. Snapshots. in the beginning your soldiers have terrible aim. When your Aimed shots has a 45% hit chance and the snapshot around 30 for about half the price its better to bombard them with snapshots. Auto Shots are only viable in close combat.
3. Kneel. It costs 2 TUs to either kneel or stand up but it decreases the chance of being hit and increases your hit chance. take that time.
4. if you didnt shoot down the UFO you'll have to deal with more aliens. You'll also get more loot if you clear the site also if you manage to get more kinds of Aliens read their descriptions. you'll know what weapons to use.
5. Dont move too far. keep TUs for Reaction shots. if they move through your Line of Sight they your guys will have the first strie
6. Try to land at your crash site when its lighted. AT night your sightlines are shortened drastically.

with that said, good luck.
one last thing - you need at least one Soldier to fly the Skyranger back. if all soldiers are killed, the Ship is lost as well. you dont want that to happen, it costs 600k you dont have that kinda money at the start. If you pull out everyone not in the Skyranger is lost as well. but at least you keep the ship.

If you managed to clear the UFO site you'll salvage the Wreck. All corpses and ship parts are brought home and are ready to be R&D'd and all injured soldiers will be hospitalzed.

if we speed up the time again our Laser Pistol Research should be completed. You'll get a report sheet for it and will be able to start the Laser Rifle Research. you also get the Message that you can now produce laser Pistols. Start the Laser Rifle Research (this is the most effective base weapon since it does not need any ammo) and head to the Production tab. Here you can make your engeneers work on your finished research projects.
Start to build Laser Pistols. they cost a few thousand each. Use all engeneers and build around 200 of them. why? I'll get to that in a bit. You'll see a number looking somewhere like this 220/13
that number shows how long they will work on that project until all are produced. in that case 220 days and 13 hours.
why should you produce so many of them, you only have 8 soldiers at best. They sell for around 20000 each so this is your method of Money making. buy more engineers if you can to increase productivity.

However, Ive been informed by the User MBGucky that laser Pistols are not the best way to go.
While we HAVE that technology we should churn out as many as we can but for optimal gains, we should be switching to Motion Sensors.
Why? Math Time!

The Laser Pistol sells for a Profit of 12000$ and is produced in 300 Workhours. this equals to about
41$ per Hour.
the other Items we get from our initial researches are Medikits and Motion Scanners -
One Medikit sells for a Profit of 18.500 with 420 hrs of Work, averaging about 44$ of profits per hour, which in itself is better. but a laser pistol "only" takes up 2 workshop spaces (instead of the Medikit 4) and needs way less time to be done.
and then there is the motion scanner. honestly a friend if youre trying to find that last alien especially in later missions, but also a real cash cow.
you can make a Motion Scanner in 220 hrs, that brings 11600$ in Profits, equaling 52$/hr
so not only is the thing faster than both the rifle and medkit it averages quite a bit more cash.

continue working like this until january ends, you'll get a result screen and money from the Council.

if your score is negative, you have been missing quire some UFOs or suffered heavy casualties in your Battles. If countries are especially unhappy with your performance they will decrease their contribution or drop off the project altogether.
they will get unhappy if UFO activities over their countries are not taken care of (Coverage, I tell you)

if 5 or more countries have dropped off the project is cancelled and the earh is doomed to a gruesome demise.

If your second base gets finished buy an Interceptor, Weapons and ammonition for it, you have your first outpost. keep Researching and producing, some of the Ailen Gear can be sold for good amounts as well. If you once again have enough money to safely expand, do so. Big land masses and lots of Radar coverage.
continue like that until you have your 6 base slots full.

if you manage to get enough Researchers and/or Engeneers to reach max space (50 per Lab and 50 minus project base cost for workrooms) build new ones. you later need a cryo cell in your Skyranger base to capture alens.

Terror Camps and Bases : That is something you REALLY want to avoid. If you leave countries unatended for too long Aliens will land and start Terror attacks in cities.
here you'll face a Multitude of Aliens in addition to Civiliand and the worst thing of all Cryssalids.
They attack in close combat only and have a good chance to poison ther targets. If a target who is poisoned that way dies he will give birth to another one of those suckers. And they just love to attack those Civilians with their 20 HP. which may result like that

A base is like one of your bases, just for Aliens. Bases swarm with lots of aliend of different races. However you dont have to kill every Alien in here, there is a 2nd Victory objective : Find the base Center, a room with a huge, organic computer, and destroy it, fastest way is with a Grenade.

During tha later game process Alien ships will try to Find and destroy your bases. thats what your defenses are for. If they dont manage to shoot down the UFO you will have to defend your base if Soldiers are stationed or just forfait it otherwise. A Warning - If a room is destroyed too much during the battle for the base the room is lost

the main reason for failure in the first few months is that countries will drop off because you dont take care of their UFOs. once again, Radar Coverage is your most important issue in the Beginning. If you manage to get past April without any country dropping out, you're on a good way.

You should have the knowledge about Battle and the general defense of Earth you need. Good Luck, Commander. and Godspeed.