Harbor Freight Tire Changer
I would like to start by mentioning a few additional items you may need to help change tires. Tire lubricant makes dismounting and mounting the tire much easier. Lubricant can be found at higher quality auto parts stores such as NAPA. When you balance the tire you will also need weights. I get mine from a local mechanic or from Flanders. Flanders is a great source for many motorcycle related items.
Here is the Harbor Freight tire changing unit all setup and ready to go. The bead breaker is facing the camera. There are some anchors in the floor that I normally bolt the unit to when I'm working with it. You can see a couple of them on the right side of the unit. Not a pretty site are they. That was my first experience with an impact drill and I didn't do the best job in the world. :-)

This picture is a close up of the bead breaker with my 2x4's laid out. The 2x4's will hold the tire flat with the bead breaker and also keep the brake rotors from getting bent by contacting the concrete while breaking the bead.

And a slightly different angle.

This picture shows a necessary modification to the tire changer. When shipped from the factory, the rim clamps face outwards. I turned them to face inwards so that they will actually hold the rim. I also put Plasti-Dip on the rim clamps to help prevent scratching the rim.

Below is the bead stop I use when mounting tires. In later pictures you will see it just clamps onto the rim. Its job is to help prevent the tire from turning on the rim while it is being mounted. The black thing on the left is an piece of an old inner tube that I use to prevent the bead stop from scratching the rim.
Note: I've had several inquiries about where to find this item. This one came from J.C. Whitney, but they no longer handle the item. I did some research on the web and could not find another source for it. However, the bead stop can be easily replaced by a small C-clamp, vice grips, or any other tool that will clamp onto the rim.
21 Aug 07 - Update! Jim from the Aprilia Forums pointed out that Aerostich now carries the Bead Buddy! The Bead Buddy is an improvement over the tool pictured because they used a plastic bolt instead of a metal one to protect the rim.

The bead breaker has a tire lined up and ready to go. The next step is push down on the long bar to break the bead. You may need to turn the tire and use the breaker in several locations if the tire is really stuck to the rim. Note: Be sure not to position the breaker right over the valve stem. The breaker could damage the valve stem.

Now the rim is installed on the machine and I'm ready to remove the tire. Yes, this is a picture of the front tire. I neglected to get this shot when I changed the rear tire. :-)
Here is a picture of the long bar used to dismount the tire in the position that I like to start in. From here I'll start pulling the bar clockwise around the machine. Use the silver, vertical bar that runs through the center of the hub as a lever while you pull the long bar around.
At this point, I have removed one side of the tire from the rim and am setup to remove the other side of the tire. Just like before, I'll pull the lever clockwise around the tire until it comes completely off the rim.
The old tire has been removed from the machine by raising the silver bar and sliding the tire out. The rim is ready to have the new tire installed. Place the new tire on top of the rim (make sure that the rotation is correct!) and lower the silver bar back into place. This picture also give a good view of how the hooks on the tire changer grip the rim.
The new tire is in position and ready to have the first bead put on the rim. Note the position of the bead stop and the long bar used to mount the tire. If you think of the red bar that goes over the tire and holds the silver bar as being in the 12 o'clock position, then the bead stop would be at about 5 o'clock and the mounting bar at about 7 o'clock. From this point I will pull the tire mounting bar clockwise until the first bead is completely seated on the rim.
I'd like to make a couple of points that are not directly related to the tire machine. When installing the tire be sure that the tire's direction of travel is correct. Also, if the tire has a mark for its heavy spot, ensure that this part of the tire is mounted opposite to the wheel's heaviest spot. Doing this will make the process of balancing the tire/wheel later a bit easier and potentially require fewer weights. If you do not know where the heavy spot on a wheel is simply use a balancing machine or static balancer to determine the spot and mark it. Optionally, you could simply assume that the valve stem is the heaviest part of the tire.
The first side of the tire is mounted on the rim and everything is setup to mount the second tire bead. As the second bead is placed on the rim, a trick to making the rest of the tire easier to mount is to push the mounted part of the tire so that is drops into the center part of the rim. This provides an extra inch or two of space for pulling the tire onto the rim at the end.
The wheel is now ready to be removed from the tire changer. To do that I raise or remove the silver bar that runs through the wheels hub area and release the rim clamps.
That is all there is to it! All these steps may sound complicated, but after you have used the tool a time or two it will become second nature. I can change a tire in about 5 minutes if I have my act together before I start.
The next task is to air up the tire and balance it. I use the balancer unit sold by Mark Parnes. Here are a couple of pictures that show a Futura's rear tire setup in the balancer. I have a short write up of the balancer here.