1) I usually take the door off the hinges and put it on sawhorses to paint. It's a lot easier that way if you can manage it.
1)Take the hardware off
2) sand all of the old paint lightly(if it's in decent shape) with 100 grit sandpaper
3)Wipe it down with a wet cloth or a tack cloth to get rid of the dust
4)Prime it with an exterior latex primer like Kilz 2 with a 2 1/2" or 3" nylon brush
5)Wash the brush and let it and the paint dry
6)Apply the first coat of an exterior latex semi-gloss paint of your choosing(if on horses let one side dry then flip)
7)Wash the brush and let it and the paint dry
8)Apply second finish coat, clean the brush, let the paint dry, and re-install the hardware and the door.
I wouldn't worry about tape. It's $5 bucks a roll and wastes time. Get a paint scraper and scrape the paint off the windows when you're done.
Brush tecniques:
Cut in around the windows first, and around any raised or set in panels, then paint the rails and stiles.
Use long, steady strokes, and paint from the wet area.
Once I get one section done I run over the whole thing in one stroke to have a nice, consistent brush line. You'll get the hang of it.

2) I don't think I can add anything to what the first comment says. That is awesome, detailed advice. I did want to let you know that there is a ton of painting to do here once you perfect your technique. :P

3) I agree with forgetting the tape - don't worry about paint on the windows, it will scrape off easily once the paint is dried. You want to make sure you get a good layer of paint where the glass and wood meet and to do that you have to paint both the wood and the glass where it meets the wood.

4) Thanks for the advice. I'll keep everyone posted on the progress.