Seems like quite a big project to start with.
My advice would be to start by developing code to control the motors to start with, possibly using up/down and left/right controls. This will teach you how to manipulate the motors whilst you're doing it as well as working out timings. Here is a tutorial for a car http://arduinoarts.com/2011/08/arduino-tutorial-f1-rc-car-dc-motor-driven-by-mos-transistor/
here is a basic motor tutorial. http://www.oomlout.com/oom.php/products/ardx/circ-03
it includes wiring, explanations and a breadboard layout.
Then incorporate sensors to control the motors. I'm not sure what kind of avoiding action you want, but you can probably use just a few photoresistors to do the job in a very basic way i.e. stopping, reversing/turning, then repeating this if the obstacle is still in the way and continuing if not.
P.s. I'm not sure why you're using led's and havent wired up a motor yet. If you are a complete beginner, work through these tutorials before doign anything else (its how i was taught basic arduino at uni this year) http://www.oomlout.com/a/products/ardx/
youll just waste time trying to do something too hard.
Example pseudocode once you know how to control the motor:
if (sensor says there is an obstacle in the way), stop
turn car (using two motors-one going left and one staying straight/going right)
stop car a few inches back
go forward in a straight line until more obstacles are met
repeat avoiding code
this is just one way to do it if you have say two sensors at the front.