How is the impeachment of federal judges similar/different to that of the president?

Yep, it's the exact same process. The U.S. House of Representatives passes Articles of Impeachment by a majority vote, which is comparable to an indictment in a criminal court. The Senate then holds a trial for the indicted judge, and if at least two-thirds of the Senate votes to convict him of what the House has charged him with, the judge is immediately removed from office.