When painting the trim, you don’t have to be neat. Just concentrate on getting a smooth finish on the wood. Don’t worry if the trim paint gets onto the walls. You’ll cover it later when painting the walls. Once the trim is completely painted and dry (at least 24 hours), tape it off (using an “easy release” painter’s tape), then paint the ceiling, then the walls.
For interior jobs, make sure you've cleaned all of the awkward spots, including behind the toilet, and picked up any knickknacks that might get in the way (e.g., soap containers, loofahs, and kitchen organizers). Removing the switch plates and outlet covers from the walls also goes a long way toward speeding up painting time—and painters' time is (your) money.