How can I animate a car driving? Is there a way to control the car like you would in a videogame?
there are some commercial solutions out there: A guy called blazraidr has a car rig, info is here: https://www.youtube.com/channel/UCBTVDEpwT5L3TXMYZO3Rn_g
I hold a completely finished car inluding a rig at my blendermarket portfolio; if you don't want to purchase it, you can have a look at the descripition video, which - if you take a close look - will show you how to setup such a rig: https://www.youtube.com/watch?v=mclrTtmJC0s&feature=youtu.be
finally, there is a simple rigged car at blendswap that might help:
Fully working car driving example can be downloaded from here: https://www.blender.org/manual/game_engine/physics/types/vehicle.html
Just download the zip, open the .blend and hit P to drive.