This How To Balance Motorcycle Tires article will help make sure the wobble wont happen to you.
If you are replacing your own tires, you probably will be interested in balancing them yourself as well and this article will guide you through the process. Like mounting your own tires, balancing is easy to do and requires only minimal tools. I will cover a technique known as "static balancing" which relies on gravity to find the heavy spot on your wheel. Most people are more familiar with the other balancing technique refered to as "dynamic balancing" which uses a machine to spin the tire at high speeds to determine balance. Unless you are planning on opening a tire shop, you probably will not want to spend the money on a dynamic balancing machine or devote the floor space to one for just changing your own tires.
As you can see from the picture, there isn't much to a static balancer, just a frame and a horizontal shaft for the wheel to rotate on. If you like doing a little bit of light fabrication, you can certainly build one yourself and can even use your own axle for a perfect fit. For everyone else, you can pick up a factory made stand for ~$100 online. These factory made stands are made "universal fit" by using a small diameter shaft with two cones that fit into the axle sleeve on either side of the wheel. Once the cones are locked down to the shaft with a set screw, the wheel is centered on the shaft and ready to be balanced.
Since you typically only balance motorcycle wheels after installing new tires, I'll assume you already have the wheel off of the motorcycle and go straight into the balancing process.
Step 1: Make sure that your balancer is sitting on a stable surface and the shaft is level. I find that a standard 9" magnetic level makes this process a whole lot easier.
Step 2: Remove one of the cones from the balancer's shaft before sliding the shaft through the axle sleeve on the wheel. Then slide the cone back onto the shaft (narrow end first) and firmly tighten the set screw to lock it in place. It is important to make sure that both cones are fitting inside the axle sleeve, if not the wheel will not be centered on the shaft which can effect the balance.
Step 3: Thoroughly wipe down the rim with a good degreaser. This is important for two reasons: first you don't want any globs of grease throwing off your balance and secondly if you are using adhesive wheel weights you want to make sure that they stick on well. Also, if there are any remaining weights from previous balancing, make sure to remove them.
Step 4: Gently spin the tire and let it come to a stop on its own. Gravity will cause the tire to stop spinning with the heaviest portion at the lowest point. Take a piece of masking tape and mark this point on the rim. Simple Green is an excellent way to clean off any dirt, grime or grease from your wheel.
If the heaviest portion of the wheel is at the lowest point, then it stands to reason that the lightest portion of the wheel is at the highest point. Therefore you will be adding weights to the top of the wheel, directly across from the heaviest portion. Adding a piece of tape makes it easy to remember the location of the heaviest point on the wheel. If you are using a non-spoked rim, your best option for weights is the adhesive backed variety that just stick to the rim. These are cheap and easy to use and allow to you spread the weight out on either side of the rim. If you are using a spoked rim, you also have the option of spoke weights with crimp to the spokes or are held to the spoke with a set screw. These tend to be more expensive than the adhesive backed weights, but they do have the advantage of being reusable and less likely to come off.
Step 5: Add a few oz's of weight to the lightest portion of the tire. If you are using adhesive backed weights, use tape to hold them in place temporarily. Adhesive backed weights come in strips that can be cut apart to achieve the desired weight. Spoke wheel-weights come in various weights and can be stacked if needed.
Step 6: Rotate the tire until the lightest portion and the heaviest portion are located equal distance from the work surface and gently release the wheel. Again the wheel will naturally rotate to a position where the heaviest portion is at the lowest point. Typically this will be the same point that you determined was the heaviest portion of the wheel initially, which means you need to add more weight to the lightest portion. Alternatively if the portion you just added weight too is now at the lowest point, then you added too much weight and need to remove some. Using double-stick tape or masking tape to temporarily hold the weights in place during this process.
Step 7: Continue to repeat Step 6 until the wheel no longer rotates on its own when released. A properly balanced tire should stay still when released as there is not a heavier portion to pull the wheel around. When you think you have the balanced correctly, try rotating and releasing the wheel (using the tape as a guide) at the 12:00, 3:00, 6:00 and 9:00 positions.
Step 8: If you are using spoke weights, you are now finished balancing your wheel and can remove it from the balancer. If you are using adhesive backed weights, use a piece of tap to mark the edge of the line of weights before removing whatever is temporarily holding the weights in place. Then simply remove the backing paper from the weights and press them firmly onto the rim to hold them in place. A balanced tire should stay still when released no matter what position it is in.
One thing to keep in mind is that it is pretty tough to get your wheels perfectly balanced since wheel weights come in fixed sizes that may not add up to the weight you need. Of course you could file the weights down to achieve the exact weight, but I don't think you'll notice much difference on the road to make it worthwhile unless you plan on running at high speeds in a race type scenario. At that is left now is to remount the wheel as per the manufacturer's instructions and go out for a test ride.