A lot of my colleagues do it. (I'm a DINK - double income/no kids, so I haven't had to).
You have to have your permanent license - pass part 3 of boards, apply to State Medical Board. Then you talk to recruiters and they have forms you have to fill out as well.
Usually the opportunities are in EDs, often rural or sometimes in town but at the VA hospital, etc. Some of the IM residents were moonlighting at SNFs - I guess they would have a doc-in-a-box on site at nights.
The EDs would pay about $60 an hour; if they were desperate you could talk 'em up to 70 or 80. That includes insurance coverage. I'm sure this varies by region.
Usually the shifts were for 24 to 48 hours straight, so you slept in a back room while you were there. Usually pretty quiet, but rarely some real excitement. My classmate triaged several family members from a car crash - intubated, central lines, chest tubes - before transferring to our trauma center. You are there without any back up at all, so be ready to treat crashing MIs, respiratory failure, trauma, so forth, although typically you're more likely to see rashes and broken bones.