start at the grassroots level. volunteer for the local campaign of the presidential candidate of your choice. be a gopher, work voter registration drives, etc etc.

I did my undergrad at GWU (not too long ago, graduated in '05).

Check out the Career Center. They were incredibly helpful for me. And also get to know your professors--both in the PoliSci and Econ departments. I'm biased towards the Econ department since, well, my major was Economics and IA.

Since you're already in the area, ask about summer internships, and possibly internships during the year. I'll be honest; I think a PoliSci degree isn't that good unless you get some real experience under your belt. (Econ degree is your other major, though, so both those plus an internship should give you a good background.) Though, talk to folks at the Career Center for another opinion.

For policy making, I think an internship at a think tank, research institute, or something similar would be optimal. For campaigning, well, any politicians' office would be a good option. Most people I knew who did that would work for the congressman from their home state/district--you could look into that. KF

This also occurs to me as I reread the original post...

Campaigning can be rough work. If you do decide to work on a campaign trail, realize that it's a temporary job (which may, in fact, be a good thing considering your school schedule), that you have to be thick-skinned, and that you may be working crappy hours for low pay. For that last reason, you also want to only work on the campaign trail of someone you actually like.

It can be rewarding work, and a good experience. But be aware of what's in store if you decide to do it. KF