Basics.

Speed boost. Press Q when your line meter at the bottom of the screen has some orange in it. The more orange, the more boost you have.
Roll: Press space bar when you hit the ground. (Or T? For some reason if you press T when you hit the ground you also roll)
Climbing. Hold left click and sprint to a wall. Space to pull yourself up, T to let go.
Sprint: Just hold Shift.
Vaulting. There are 3. For a cat pass, hold left click and press/hold R.
For a speed vault, same thing but press F instead of R.
For a reverse vault 360, same thing as speed vault but T instead of F.
Dash Vault: Left click and Space.
Wall run. Sprint, jump and hold left click. Press space again to jump off.
Wall slide: hold left click on a wall. It resets your fall height.
Precision Jump. Hold E to charge, when you hit the ground press E for a stable landing.
Swinging. Hold left click near a pole.
Slide. Press X while sprinting.

Holding 1 allows you to change the weather to rainy or sunny, and switch to pigeon mode and skip to next soundtrack.
Holding 2 sets the session marker, pressing 3 teleports to the marker.
Pressing 4 makes you ragdoll.

Now onto pigeon controls.
Space makes you go down when flying.
Double taping space toggles flight.
WASD to move forward backward left right.
F makes you fly up.
Q to barrel roll left.
E to barrel roll right.

Wave: hold R
Point: hold F
If the game is a Push game press 4 to push.

Tricks. You kinda gotta be precise with mouse movement btw. Also you need to sprint for 90% of these tricks.
Stride. Hold left click when you see a bunch of horizontal beams.
Dive roll. Sprint and press T. If you hold left click it will not work. You also can't really fall very far without ragdolling, keep that in mind.
Front flip. Jump from somewhat high up and hold R and move your mouse up
Dive FF. Same thing, but move your mouse down.
Cartwheel. Press R and sprint.
Back handspring. After cartwheel, press T. You need to press it after the cartwheel is almost finished.
Death Dive. Same thing but move your mouse left.
Spin 360. Hold F and move your mouse left. Keep doing spins for a higher number.
Vortex flip. Hold F and move your mouse right.
Side flip. Hold F and move your mouse up.
Cork backtwist. Hold F and move your mouse down.
Backflip Jesus. Tap space 2 times in rapid succession and move mouse down
Gainers. Tap space 2 times in rapid succession and move mouse up or left for loose gainer, right for normal gainer.
Illusion Twist. Press G when sprinting.
360 Dive Roll. Press F than shortly after T.
Airball Backflip. Do a cartwheel than press F.
Airwalk Backflip. Do a cartwheel than press left click and F.
Cork. Left click and R.
Chain Precise Jump. Do a precise jump and a precise land and press space as you land.
360 Gainer. Space and mouse left.
360 Frontflip. R and mouse right.
Standing Backflip: Press E and F when standing still. Press E first though.