I used to drive a ’93 Volvo and self-transmission flushes were common.
Materials:
About six feet of clear flexible plastic tubing, 3/8” ID if I remember right. A transmission funnel. Enough transmission fluid to cover the volume of fluid in your transmission, plus a couple extra quarts. A few milk jugs, marked with a permanent marker to show quarts (add a quart of water to find this line, etc).
OK, this is the tricky part. Find the line that goes from the radiator cooler to the transmission, disconnect it and put your plastic tubing on the nub on the radiator. It will be a snug fit. Put the other end in a milk jug on the driver’s side of the car. Remove the transmission fluid dipstick and put the funnel in there. If it doesn’t fit get a different funnel, but if you are using a transmission funnel it will fit. Open up a few quarts of the new fluid. Start the engine. Transmission fluid will be pumped into the milk jugs. As fluid enters the jug be adding fresh fluid through the funnel – keep the level of fluid pretty constant (for each quart out have one quart of fresh fluid in, that’s why the milk jugs are marked, so you can tell pretty accurately how much has come out). At some point shift the transmission to each gear for five seconds or so. Eventually you will see fresh transmission fluid going through the hose (which is why you want a clear hose), at that point turn off of the engine, reconnect the cooler to the transmission, let the engine run a little and check the fluid level.
Take the used transmission fluid (in the milk jugs) to your local mechanic, they will take it at no cost.
Here are some instructions for Volvos if you wanted to see a more "official" writeup:
http://www.brickboard.com/FAQ/700-900/TransmissionAuto.htm#7XX940FluidFlush
http://www.ipdusa.com/uploads/sku_files/5310_INST.PDF
Besides my Volvo, I did this on my '95 Toyota Camry. My current cars are both manual transmission so it's been a few years since I've done this.
Note that the filter was not changed. On the Volvo it was recommended to not change the filter unless you were having transmission issues. Changing it just increased the chance of a leak.
Edit: this is close to what d-machine describes above though I wouldn't do three quarts at a time. Just let it drain (pump) constantly while adding fresh fluid constantly, until the fluid leaving the system looks "new".