Technically, the rules are wide open: In both the House and Senate, expulsion requires a two-thirds vote, but the Constitution allows both houses to expel members according to their own, self-created rules, without consent from the other chamber, as long as the two-thirds requirement is met. But Congress is typically reluctant to invoke that power. As Supreme Court Justice Joseph Story once noted, expulsion is "so subversive to the rights of the people" that it should be used sparingly and be "wisely guarded." The threshold is pretty high, and the offenses have to be quite bad.
Here's a list of what a lawmaker must do, according to historical precedent, in order to actually get kicked out:
1. Support the Confederacy. The vast majority of expulsions had to do with secession and the Civil War, occurring in either 1861 or 1862. Of the 20 expelled, all but three (two representatives and one senator) were kicked out for backing secession. Aside from secession being considered generally treasonous, there was a practical matter at hand: The Senate ran into problems attaining a quorum, and, since the Union was fighting on the premise that Confederate states were, despite their saying otherwise, part of the United States, the Senate's solution was to kick out individual senators, reducing the size of the body and therefore the attendance-number required for business to proceed, rather than simply ignoring the existence of Confederate states.
2. Take Bribes From the Mob. It seems that, to get expelled from Congress, one must demonstrate a widespread pattern of corruption, but bribes from organized crime appear to help. Ohio Democrat Jim Traficant was expelled in 2002 following conviction on 10 counts of racketeering, bribery, and tax evasion, after he lobbied federal officials in exchange for contractor work on his horse farm and was found to owe up to $180,000 in unpaid taxes. But bribery seems to have done him in: he took $108,000 from organized crime and demanded kickbacks from his staff. Some of the back taxes, in fact, were owed on money paid to him by organized crime.
3. Offer Political Asylum in Exchange for Cash. The only other non-Confederate House member to be expelled, Pennsylvania Democrat Michael J. Myers, was booted in 1980 for taking bribes in exchange for immigration lobbying. Specifically, Myers was caught in an FBI sting accepting $55,000 cash (in an envelope) from an agent posing as a sheikh who sought asylum in the U.S. Myers fell for it, promising to either introduce a bill in Congress, or lobby the State Department, to allow fictitious sheiks to enter the country for political asylum. He was expelled in 1980.
4. Plot Against the Spanish Government. In the weirdest expulsion case, Democratic Republican Senator William Blount of Tennessee got kicked out after being accused of anti-Spanish conspiracy. According to the allegations, Blount colluded with a British agent in a plot to seize control of Spain's territory in Louisiana and Florida. Blount was expelled in 1797. As a consolation, he was elected president of Tennessee's State Senate during his impeachment trial.