When would I use this?
1. There is a lot of car over there.
And when would I use this?
2. There are a lot of cars over there.
How do I know which one to use? Does it matter?
1. is incorrect. 'car' is a count noun so it needs to be plural, as in 2.
Here's how you know which one to use:
There is a lot of money, fish, traffic, milk, etc. (non-count)
There are a lot of cars, books, pencils, people, etc. (count)
There's a lot of books.... (OK; informal)
A singular verb is often used in contracted forms: Contracyed "There's (a lot of books)" is OK, but "There is (a lot of books)" is odd. The reason a singular verb is used with a plural subject has to do with ease of speech. "There's" is way easier to pronounce than "There're". Give it a try! :D