1) Clinic needs shifts covered.
2) Doctor wants to cover the shifts to make money.
3) An hourly rate is agreed upon by both parties.
4) Perhaps an email is exchanged memorializing the deal.
However, in the Age of ACA and HIPAA and other alphabet soup, things have changed. It is unbelievable the kinds of contracts that I'm expected to sign nowadays for the privilege of serving the sick and injured (no sarcasm intended) in order to make a few extra bucks to support my expensive poetry habit (insert sarcastic inflection here). The indemnity clauses alone are enough to make one have to go to a clinic--as a patient! I won't sign. So, I don't work. And when my private practice is slow, I can't buy poems. Or pay bills.
On the plus side, I "found" three hilariously ironic poems in one of the locum tenens contracts that I recently refused. All I had to do was replace "Physician" with "Wizard," "Locums Company" with "Abaddon Corporation" (I was going to use "The Devil" but did not want to be too obvious), "prescription drugs" with "potions," "healthcare" with "magic spells," etc etc and voila! Satirical speculative poetry!
Take that, Abaddon Corporations! You know what you did! Someday you'll need a doctor--oh yes--then we'll see who's going to sign whom's one-sided deals with the dev...but I rant, don't I?