Hi,
Cut in no more than necessary. If you do the walls first, you can probably get by with cutting in the casings once.
Use a roller to apply trim paint, then brush out. Don't spend the effort in getting the paint on, but in getting it smooth.
Use floetrol when necessary, it can be a great labor saver.
Use covers to protect things that don't need paint! Less time spent cleaning self-inflicted messes is money in your pocket.
Practice "doubling up" for low-coverage semi gloss paints. This means putting on the second coat before the first cures up hard (and slippery- the next coat will slide and not grab).
Use a hvlp sprayer and do all the doors at once in a garage or unfinished room.
The better painters in this group will have more suggestions.
Casey

sombreuil_mongrel: thanks for all the tips so far. I have never heard of floetrol. In what way is it a labor saver?

Hi,
Floetrol is an additive for latex paint that helps with brushing it out. In hot weather it makes it possible to brush out latex w/o it getting ropey- i.e.; drying on contact. It retards the evaporation of the water from the paint. Use as directed.
Casey

Paint the trim before the walls. It's easier to cut into the trim paint with wall paint than the other way around.

If you have any control over paint color choices, go with colors that do not have high contrast. Some people even like the look of trim and walls the same color. That's a real time-saver, but it can look a little budget-conscious in some homes.

Learn where best to stand to get the right angle on a door or window when you are cutting in the edge to the wall. Relax, and let the weight of your arm and the brush help you draw an even line on the downstroke. Don't waste time with tape. Take a breath and exhale with the downstroke to help keep your hand steady. It's very zen, Grasshopper.

Use a small roller and grid in a 1-gallon can to do large areas like shelves, doors and cabinets. This is a good system for doing a handrail or pickets quickly, especially if you can have one person on each side, moving in unison.

Standardize as much as you can. Find a good quality paint you like and stick with it. Have a system for doing each door and window, so you won't waste a single stroke. For a window, for example, I move the upper sash down, do the lower half, raise it, do the upper half, do the outside lip of the sill, then paint the the lower sash, starting with the bottom edge. Do the edges of the window trim, then the top and each side, and finally the sill. Some painters even time themselves, say, per doorway, then try to beat their own time. Wear a watch and stay aware of minutes.

Keep all your tools and supplies organized and clean, so you don't waste time hunting for things. Wear your tools -- a rag, a 5-in-1 tool, a duster, a small screwdriver for removing switchplate and outlet covers, some putty, sandpaper. Carry a workbucket with only a few inches of paint. Wear comfortable shoes and clothing.

Practice, practice, practice. You will develop your own style and shortcuts. Good luck.