We started by taking down all the doors off the cabinets, and laying them flat on a tarp in the second bedroom:
Then we had to sand them down. Joe at Thybony Paint instructed me (thanks, Joe!) that we didn't need to sand them down completely -- just scuff them to break up the varnish to allow the wood to absorb the paint. This was a task:
Once they were sanded we could get to work. So we turned on KCRW (thanks, Internet!) and got to it. Dave rolled, and I followed with a brush to do the details and finish edges. We are using an oil-based paint, and I was assured by both Joe and the Internet that we didn't need to prime. Our color is Simply White, and it will have a eggshell, semi-gloss finish.
Here's the first coat: