Damil above is correct in needing a PhD or Masters degree then publishing your own research. It wouldn't be common to hire an individual without experience in such a demanding environment as you need to be able to do more than read articles and history, there are test to be ran, and numbers to crunch, and experts to seek out. Building rapport with someone in that field is critical as well.
From my knowledge as a political science graduate in order to become a political science researcher for a major university, having a good relationship with an instructor is important. During your undergraduate career if you pursue a major such as political science or history attending office hours for a professor can help get the process started. Your aim should be to get a summer internship with the instructor or within the political science department as a researcher. Another avenue to become a researcher would be to pick a specific issue/topic you would like to study and pursue it with an instructor when electing to write your senior thesis. Speaking with professors at your college and university will point you in the right direction depending on where you live. Getting a masters degree or Phd may be required for specific universities, speaking to your local career center or political science department may help.
Hopefully this helps,