Most students have the option to register to vote at either their home address or their local residence. It's important to decide where you will register, as some states are quite lenient and allow same-day voter registration and absentee ballots while others are stricter and require registration a month before the election and restrict out-of-state voting.
Information about voting and registration in all 50 states can be found at vote411.org. The "Voting in Your State" section is particularly useful because it provides deadlines and residency requirements.
The "Register to Vote" button brings you to a page that asks you to provide your email address, to either enter your zip code or choose your state from a drop down menu, and to select register to vote from the list provided. Once you have supplied this information, you will be taken to a registration wizard that will walk you through the voter registration form for your state.
You might also want to use the "On Your Ballot" section of the vote411.org website to learn about issues and candidates in your state. Once you enter an address and zip code, the website will provide local candidate biographies, positions, and major issues in the election.