The process can be broken down into two steps:
1) Installing the new spokes
2) Truing the wheel.
I found it made my life a whole lot easier to build a truing stand out of cheap lumber. It was fairly easy and worked great..
Installing the spokes.
There are 36 spokes in the rear wheel, arranged in pairs. 18 pairs per side.
Look at the hub. You will see two sides. Each side has 9 pairs of spoke holes drilled. Each pair consists of an "inner" and an "outer" hole.
Each spoke pair is in a criss-cross arrangement with on one top of the other. The spoke that crosses on top is the "outer" spoke of the pair, while the other one is the "inner". An "inner" spoke will *always* attach to an "inner" hole on the hub. An "outer" spoke will *always* attach to an "outer" hole on the hub.
Strategy: working your way around the wheel, and alternating left and right side, install all the "outer" spokes first. Then do the same for the "inner" ones. When installing spokes, grease the nipples, and don't tighten anything! Just get the threads started. Tightening will be taken care of when you start the truing phase.
Truing the spokes.
Start at the valve stem, tighten every third spoke so that all the thread slack is taken up and it's just starting to tighten. Back at the valve stem, jump to the next spoke and tighten every third one as above continue until each spoke has been done. Don't turn each spoke more that about 1/4 turn each time. The trick is to take it slow and do things evenly and gradually. It make take several passes to get all the spokes to the right tension. Don't try to tighten down all at once. As things begin to get tight, keep an eye on the run-out to be sure you don't pull the rim out of shape. You want to keep an eye on side-to-side run-out and the radial run-out . The pros use dial indicators to do this, but you can set up a wire or a rod to use as a fixed reference to eye-ball it.
Some good references:
http://www.fasstco.com/html/spoke_tips.html
http://www.off-road.com/dirtbike/nov00rsWheelTruing.html