For the most part, your post-award requirements won’t be very demanding during graduate school. When you receive an award, make sure you save the letter from the sponsor, which will outline any requirements and conditions during the project period. In general, expect to be required to submit two things by the end of your grant:

1. Final Report: This is usually a fairly short — just a couple pages — narrative in which you explain in detail how the sponsor’s funds helped your research, what progress you made, what you did, and your plans for completion of the project (if it isn’t finished) or for publication. The award letter will outline exactly what information they want. If it doesn’t say, give an overview of what you did during the period of support.
2. Cost Accounting: Expect that, for the money you’ve received, you will need to prove that you spent it. Save all your receipts for gas, air travel, ground transportation, accommodations, microfilm purchases, photocopying, etc. A sponsor can ask for any and all receipts. If you don’t spend all the money awarded, you will have to send it back. That’s fine. Don’t fudge your expenses, and don’t include items that aren’t allowed, such as food or entertainment. Just use sound judgment and have meticulous record-keeping, and you’ll be fine.