A lot of students freelance. You might want to start out advertising on CL for local businesses. It will be slow initially, but you will pick up speed.
How much do you need to make a week? How many sites do you think you can do a week? Halve that and you'll know how much you need to charge.
If your parents aren't sweating you about the money, don't sweat them. Look at your local Craigslist.
Do you need to stop taking money from your folks, or is it a pride issue? That is, can they afford it or not?
Honestly, if it's not something where you need to do it to help with the family's well being, I'd strongly consider just continuing to leech off them for a while, at least the first couple years in college. Paying your way is great, but worrying less about that kind of thing is more conducive to learning.