How do I get the stem out of a hose bib to replace the washer?
(I need to do one of these myself in the next couple of days.)

As I recall, you would follow this procedure...


Turn off the water, so no pressure is found at the valve itself.
Remove the handle, by unscrewing the small screw in the center. Be careful not to damage the phillips head recess, as this screw is probably made of brass.
Remove the small nut around the stem.
Put the handle back on. This part is only temporary, to allow you to unscrew the stem itself.
If the stem will not pull out, you need to pull out the packing around the stem. That packing prevents water from escaping past the stem when the water is turned on. You may need a needle nose pliers to pull the packing out.
Once the packing is removed, the stem should unscrew easily. Do so.
Verify that you have the correct size washer, and put the new one in. Again, be careful with that screw as it is often made of a soft metal. If you damage the head, replace it too. (If the water has been dripping for too long, the seat for the valve can actually be eroded. So look inside for signs of this. There are tools you can use to repair a valve seat, but it might just be better to replace a valve that is badly damaged.)
Screw the stem back in.
Replace the packing. New packing can be bought from your local hardware store, and it is a good idea to replace it now. It is basically cord, impregnated with graphite or teflon, that will compact under pressure from the nut.
Put the packing nut back on, not too tight that the stem will not turn, but not too loose that water comes out when the pressure is back on. Either of these problems are easily identified and resolved of course.
Put back the handle in its proper place, tighten down the screw carefully.
Turn the water back on. Check for leaks.


I think I got the major steps down.