Every person you ask will likely have a different story about how they landed their coveted job on the Hill. For me, I was a few years out of college working in the Ohio State Legislature. I told everyone I knew that I wanted to work in DC on the Hill. Low and behold, I received a call on a Friday about a job with an Ohio Member of Congress that started on Monday! "Could I get there? Yes I could!" My then-boyfriend and now-husband drove out to help me pack my stuff and made the 6 1/2 hour drive to DC.
The job was great. I learned a lot every day and met so many great and smart people. For me, it was the realization of the American Dream, from studying civics in elementary school to actually writing legislation. Back then, no one I knew started out interning on the Hill, we all had paid positions.
Nowadays, unfortunately, many people do have to start out interning just to get their foot in the door. Don't fret, though, if you do need to start out interning. Many folks have parlayed interning into full-time paid positions. Work hard, look and be smart and good things will likely come your way. You may get lucky and land a paying job from the onset. Just don't give up.
While the House and Senate do have job posting sites, most jobs will be taken before they are posted. Figure out which political party you want to work for and start reaching out to Hill offices. Use LinkedIn and other resources available to you through your college career offices and libraries. There is a wealth of information to be found online about working on the Hill.
Make sure to tell everyone you know about your interest in landing wIll job. Be bold! Good luck!