This is my first guide, so bear with me on any spelling mistakes.

This guide will instruct you on how to beat "Sam & Max 301: The Penal Zone"

I recommend trying to beat the game yourself and only use this guide on parts when you are stuck.

Keyboard Shortcuts:
Movement - W,A,S,D OR Arrow Keys OR Numpad 8,4,6,2
To Run - Hold Shift
To Pause - Space / ESC
Switching between Sam and Max - M / Q / The 'End' Key / Numpad 7
Open Your Notebook - N / C /3 / Page down
Open Your Inventory - I / E / Del / Ins / Numpad 0 / Numpad 9

Good luck, Have Fun

If you're stuck on this section of the game, You need to think quickly reconsider if you're the right kind of person to be playing this game. But here is a guide for it anyway

Sam and Max are trapped in a prison cell.
First of all switch to Max (The Rabbit) by clicking his portrait in the top right of the screen
Click on the phone toy (Teleportation) on the far left of Max's menu
Now call "Stinky's Cell"

Once you've teleported over to Stinky open your inventory by clicking the cardboard box in the top right of your screen.
Click on the "Homing beacon"
Now click on General Skun-Ka'pe

General Skun-Ka'pe will notice you and the brain will open a sphere behind you.
As Sam click on the item inside the sphere
You will now be playing as Max. Click the new item (Rhinoplasty) you have obtained (to the right of the phone)
Now click on the painting of a plant, It should be directly in front of you, or slightly to the right.
The Rhinoplasty in Max's hand show now have a picture of a plant on it. Click the Rhinoplasty

You will now be playing as Sam Again.
Walk forwards towards General Skun-Ka'pe
Once you can no longer walk forwards anymore open your inventory and select the "Homing Beacon"
Click with the "Homing beacon" on General Skun-Ka'pe

Open your inventory once again and hover your mouse over the "Remote Control"
Click the icon of a bird in Sam's hand (Activate)

Talk to "Harry Moleman" who is in the Prison cell to the left of yours
A new item will appear, go and get that.
Change to Max and then use the new item you have recieved on "Harry Moleman"
Teleporte to Harry Moleman's Phone

Change to Max and use the Rhinoplasty on the Weapon's display which is on the wall in the background.
As Sam click on Max who is now a bazooka.

Now Enjoy some Intro Credits

Go inside General Skun-Ka'pe's Ship
Switch to Max and use the future Vision Toy on the Brain and then on Sam
Click the door to your right, a moleman will walk in and go into the room on your left
Go over to the door that the moleman enterd and open the hatch to the right of the door, take all his items "Hard Hat and the Ticket)
Leave the ship

Go to Stinky's Diner (To the right of the ship)
When inside switch to Max and use your Future Vision on the character "Flint Paper"
After Watching the cutscene use the "Hardhat" you got from the mole man on "Flint Paper"
Talk to Flint until he gives you a "Mysterious Note"
Open your inventory and read the note

Whilst still in the diner go to the right and use Max's future vision on both "Stinky" and "Grandpa Stinky" and Grandpa Stinky's Radio

Leave the Diner and go all the way to left until you find your car.
Click on your car
Pick up the jumper cables from the back seat of your car
Click on the steering wheel or map and drive to "Bosco Tech Labs"
Go Inside Bosco Tech Labs

Once inside use the elevator
Use Max's Future Vision on "Harry Moleman" and "Momma Bosco"
Talk to "Harry Moleman" About Vacation Tickets.
Use the Vacation Ticket on Harry Moleman, He will give you a lottery Ticket.
Leave Bosco Tech Labs
Drive the car to "Straight & Narrow"

Use the phone in your car to Call "Stinky's Cell Phone"
Tell Her "Let's Meet" She Will Leave the Diner
Enter the Diner,
Give the Lottery Ticket to Grandpa Stinky
After he leaves pick up the "Demon Broth" from the counter
Then Walk behind the counter and press the green button
Walk over to the table that was lowerd and click on it

You are now in the Sewer
Click on the pile of junk to your right. You will now have the "Power Core" and a "Scanner"
Leave the Sewer and make your way back to The Brain inside General Skun-Ka'pe's Ship

Once you're at the brain use the "Demon Broth" and the "Power Core" On the Brain
Now use the Power Cables / Jumper Cables on the Brain

The Brain should now be alive

The Brain Should now be alive, if it's not go to the previous section

Go to the bottom floor of the Space Ship and pick up the Teleportation Toy
Switch to Max and use the toy to teleport to "Stinky's Cell"
Pick up the phone
Teleport to Sybil and make your way back to the upper floor of the spaceship

Once you're on the upper level of the spaceship (where the brain is) use the door to left where all the mole people have gone.
All of your items will be taken from you.
Switch to Max and teleport to Stinky's diner
Talk to Grandpa Stinky and tell him "We Love SkunKape"
Max will try to attack Grandpa Stinky, Exit the conversation and change to Max.
Teleport to "Stinky's Cell"

Once Grandpa Stinky has exited the Moleman Room use the Item Hatch to the right of the door ot retrieve all of your items and Grandpa Stinky's Items.( "Shot Glass" And "Homing Beacon" )
From here switch to Max and teleport to Bosco Tech

Once you Teleport to Bosco Tech Labs Sam will be thrown out of Bosco Tech, Go to the left of the building and climb up the fire escape
Once you're on top of the building go to the right and walk along the pole with the flag on it.
Click on the bird at the end of the pole, it will drop a ring
After that switch to Max and Call "Stinky's Cell"
The Ape will come with Max and fall of the building
Go down the fire escape

Once you're on the street pick up the ring (use it on Max for an... Interesting cut scene)
Enter Bosco Tech Labs. Once you enter Sam will pick up a receipt from the table.
Go down the Elevator and talk to Momma Bosco about the "Destabilizer" Then pick up the remote control from the cabinet to the left
Switch to max and Teleport to C.O.P.S

Once you arrive use the "Scanner" with your car. It will be added to thhe C.O.P.S Group.
Click on the Scanner and then use "Stinky's Cell Phone" and the "Shot glass" with the Scanner
You wil recieve a new location (Meesta Pizza) Go there.

Once you arrive go to the right of the building down the alley way and use Max's future vision on the Pizza Boxes
Switch to Sam and use "Stinky's Cell Phone" on the pizza boxes
The bird will take the phone
Switch to Max and Teleport to "Stinky's Cell"
Go to the Car and use the Scanner. Put the Engangement Ring and the PostCard in the scanner, you will get a new location (Pawn Shop) Go there.

Once you arrive at the Pawn Shop Switch to Max and use the Future Vision on the Dustbins / TrachCans
Then Switch to Sam and click on the Dusbins / TrashCans
Once you have the "Banana Peel" go to the middle of the street and use the Manhole.
Once you've lifted it out use the "Banana Peel" On the removed Manhole Cover
Enter the Pawn Shop you will recieve a "Paddle Ball Toy"
Use the "Paddle Ball Toy" and the "Receipt" in the scanner and you will discover a new location (Toy Store)

Once you arrive at the Toy Store switch to Max and use the Future Vision on Sam

....

Yep It's that Easy.
NEXT!

You will now be back on General Skun-Ka'pe's ship, talk to Stinky and ask her about her phone and herself.
Then tell her "Skunkape's not so bad" and choose "Spaceship"
Switch to Max and teleport to "Stinky's Cell"
Once you arrive you will find your plan has been ruined and you're teleported to the Penal Zone.
Switch to Max and Teleport to "Bosco Tech"
Once you arrive Talk to Momma Bosco....Or don't. Either way pick up the "Rift Generator" from the table behind you.

Once you arrive at Sybil's phone head towards the sewer entrance that is glowing, Once you get there Skun-Ka'pe will start to attack you.
Run over to Sybil's Boxes of stuff and wait for General Skun-Ka'pe's ship to try and attack you, Dodge the attack and it will creat a hole in the street
Switch to Max and teleport to Sybil's phone once again.
Once you arrive go through the "mysterious tunnel" to your left.
You will find a cult of Molemen.
Go to the left of the room and pick up the cable that is on the wall, attach it to the chest. go to the plug socket further to the right and use the "Rift Generator" from your inventory.
Now Teleport to "Stinky's Cell"
You will automaticaly get some of your items back
Now use the "Homing Beacon" on General Skun-Ka'pe
Use Max to teleport back to Sybil's phone, Walk back to where you placed the "Rift Generator" and use it.
Skun-Ka'pe will be dragged down to the generator, but he will grab onto a metal pole.
Walk over to the boiler next to the "Rift Generator" and use it (you may have to use it twice) The molemen will complain and sweat will drip over the floor.
Open your inventory and use the "Paddle Ball Toy" On Skun-Ka'pe
You have now won the game. Good job!
I hope this guide atleast helped a little!