Qualifications
You'll need a lot of education and years of study to hone your linguistic talents. At the very minimum, you should have a BA in foreign languages with a minor in political science for good measure. A Master's in foreign languages will be even more impressive, and usually necessary for higher-end jobs. You could also choose a school that specializes in international studies for your advanced degree.
The bottom line will be how fluent you are in your languages. Submerge yourself in the languages and culture by spending time in France if you speak French, or hang out in Italy if you're interpreting Italian.
Learn at least three of the big six and have a solid knowledge of politics and foreign affairs if you plan on going into something worldly like the UN or want to interpret for foreign diplomats.
If you're planning to interpret for the legal system, you'll need to get licensed as a court interpreter.
If you're planning on interpreting for the medical field, you'll need to join the National Board for Medical Interpreters and get certified through them.