How do you arrest someone in Red Dead Redemption?

Answer 1

you can't

You sort of can, you just hogtie somebody and put them on your horse then run away. The cops do go after you.

A fun thing to do is put a hogtied WOMAN on the train track and let them get run over by a train. This unlocks an achievement and is fun to watch.

Answer 2

You can't arrest someone personally but you can take out your lasso and hogtie them, and proceed to take them to the local Sheriff's office and lay them down there. Basically a citizens arrest.

If you are heartless (or obsessed when it comes to getting awards) and want to get a pretty easy trophy/achievement, then hogtie a woman, any woman, lay her down on the railroad tracks and witness her death by a train.