Like in the picture, you should aim either to the left or to the right of the direction you are trying to go.

Press W and either A or D. You should be walking diagonally, but your aim will compensate and you will walk forward relative to the direction you want to go.
[In essence, if you are walking down a long hallway, you will be walking in the right direction, but looking diagonally.]

Mash the spacebar. If on a flat surface, every time you jump then hit the ground you will go more quickly. This is called "Bunny-hopping" or "bhopping" in other games, like Quake.

Movement in old and bad games is done incorrectly. The developers seperate the W and D keys' movement from the A and D keys. In reality, if you were charging forward, then started to strafe (move left and right), your movement forward would slow.
In video games like DOOM, Duke Nukem 3D, and System Shock 2, pressing W then A or D would not slow your movement forward.

This means your total velocity is increasing. So, simply direct your orientation so that your velocity's direction is wherever you want it to go.

Example:
If pressing W makes you go 100 units per second forward, and pressing A or D adds a vector of 50 units per second left or right, using diagonals we can go even faster than 100 units per second.
Pythagorean theorem: a^2 + b^2 = c^2
100^2 + 50^2 = 12500
so, c = sqrt(12500) or 111.8

This is faster than 100, even though the developers never intended this.

Now, the jumping can be explained more easily.
Jumping forward applies a force both in the direction you are moving and up. This force in the direction you are moving makes you go faster than usual, and you will speed up every time you jump.

Look left a little bit. Hold W and D. Press spacebar very quickly.
or
Look right a little bit. Hold W and A. Press spacebar very quickly.