Peers could only be tried by, guess what, a jury of their peers. That could be the entire House of Lords, or a large committee of them, sitting in the Court of the Lord High Steward. The last time the latter occurred was a trial presided over by Judge Jeffreys. (The peer in question was acquitted.)
For a good fictional treatment, read Clouds of Witnesses by Dorothy L. Sayers.
I believe the privilege was abolished by Parliament in the 1930s.