The party leadership — both the majority and minority — assigns their members to committees. A lot has to do with seniority, but Senators are also usually assigned to committees that they either have experience with (ex: a former soldier being assigned to Armed Services or Veterans Affairs, or an ex-cop being appointed to Homeland Security or a Judiciary sub-committee). Plus, Senators from certain states want committees that their constituents care about (ex: Agriculture for a Senator from Iowa, or Energy for, say, New Mexico). You can also earn plum committee assignments by doing political favors. That’s the game.