This varies from state to state. You are allowed a certain amount of money each week based on your total earnings over the previous two years. Any money that you earn beyond the weekly unemployment allotment must be reported to the state office. (If it isn't, and the state finds out, there are severe penalties.)
The unemployment monies you have coming continue until they are exhausted. I think it's now at 99 weeks which, to lots of people, is equal to a nice vacation. Regardless, every state unemployment office has FAQs (frequently asked questions) posted on their web site. This question is asked often and the answer will be there.