How do I drive a Vehicle?

Basic driving:
"W / A / S / D"
Flying a Helicopter/Jetpack/Broom: "Space"
Flying a Plane: Look up while pressing "W" to go up and look down to go down
Change the direction of a Train: Press "S"

Opening the trunk: "RIGHT CLICK" - while riding the vehicle
Refueling the vehicle: "Shift + Left-Click"
Picking up the vehicle: "Shift + Right-Click"

Dropping bombs from the plane: "Right-Click" TNT - while flying (permission)
Firing missiles from a tank / helicopter: "Right-Click" a fire charge - while riding (permission)
Shooting with the Mecha: "Right-Click"
Grappling / Hooking with the Mecha: "Left-Click"

Enter Submarine View: "Right-Click" - while riding
Exit Submarine View: "Space"

Does your vehicle get stuck while trying to go up?

All road vehicles (cars, tanks, drills, bikes, etc) can only climb slabs and stairs. They can not climb an entire block. Bikes however can jump 1 block high, and hoverbikes can hover/climb up 1 block.