Mounting & balancing tires yourself
This process is not nearly as difficult as it seems and, like most things, it gets easier after the first time you do it. Prices charged for mounting tires at shops are usually not low. You can easily buy all the tools needed to do this for less than what it'll cost to have a shop mount tires for you once.
Note: See links to other articles at the bottom of the page, and the companion piece on balancing your tires.
Doing the tires yourself isn't bad at all. It does take a bit of physical effort and some time, and a few special tools:
Use 11" (or so) tire irons, as they're just long enough to forgive sloppy technique but not long enough to give enough leverage to easily bend a rim. Tire lube isn't strictly necessary, but most people find it does make the task easier. So, if you're going that route, buy some purpose-made tire lube. Don't try to make do with something, and do not use dish soap and water, as that stuff can and will eat at the tire. It is possible to get nasty-looking tires with gooey, melty rubber from dish soap. It's designed to attack grease and oil, and tires are a petroleum product.
Dish soap is also not kind to your wheels. After a few years, it has eaten away the rim on this one to the point that it will no longer hold air.
Removing the wheel
After you have the wheel(s) off, if you bought the tire from the bike shop you can take it there to change; they'll probably charge you 20-30 bucks to replace it. Ask how much first.
Removing the old tire
The first thing you want to do is remove the core from the valve stem, letting all the air out. Next, lay the rim on 2 pieces of 2x4, which act as a cushion from the floor and keep the brake rotor from touching anything.
This is so you can break the bead. Shown here is the 2x4 method. It's cheap, easy and works well.
As you can see, with the wheel on the ground, you use a long 2x4 to put leverage on a shorter piece, thus forcing the bead of the tire off the seat on the rim.
You're looking to see this:
The 2x4 method works best, if you have somewhere you can do it. Other methods of bead breaking include using a car jack and running over the bead with a car. C-clamps are another, less space-intensive option. Put a large C-clamp around the sides of the tire and tighten until the bead comes off the rim. You might have to do this one more time to get the other bead free.
Along the same lines is something that you might already have in your toolbox: a bar clamp or two. They work really easily. If you're buying one of these specifically for this, note that the cheaper versions have a plastic locking piece inside them. Make sure you buy clamps with a steel lock.
A couple comments on the picture below: Don't put the clamps quite so close together if you use two of them. Also, you really don't need to force the tire over very far with the clamps, as it may seem when looking at the picture. Once the bead breaks, the side that you're breaking will tend to drop into the middle of the rim by itself.
If you want to be one of the cool kids, you can get one of these from Harbor Freight. It stores somewhat compact and works many times better than a c-clamp. JC Whitney has one that appears to be the same.
Once you get the tire started off the bead, you can usually just push it the rest of the way toward the rim center. Turn the rim over and repeat on the second side.
With the bead broken, it's time to start removing the tire from the rim. Apply some tire lube to the beads. Use the sliced up plastic jug to protect the paint on your rim, and work one end of a tire iron between the rim and the tire.
To remove the tire, you need to push the opposite side (still on the top, just on the other side of the tire than the one you're currently working on) of the tire into the drop center of the rim. This is the narrow part of the rim in the middle, before it steps up to the bead. Doing this allows the tire to shift enough for the bead to slip off with the tire iron. If you leave the opposite side up on the top part of the rim it will be much harder to remove the tire, and much easier to cause damage to your wheel. Once you have the first bit over, it's just a matter of repeating the process with the other irons. Make sure you don't try to take too big of a bite, as this is where you can get into trouble wanting to use extra strength, which could bend the rim.
After you make it about halfway around, you should be able to just pull the bead off the rest of the way with your hand.
Now for the second bead. Work from the same side as before, use one tire iron, and put it all the way through.
Push down firmly.
And pull the tire off with your hand.
Inspecting rims and new tires
At this point, clean up the rim inside and out. You want to make sure the seat area (which is the flat landing just off the edge of the rim, on the inside) is clean and fairly nick/ding free. Bends, dings, nicks or junk in there can contribute to a slow leak, and who wants to deal with that? You should also check the wheel bearings by just putting a finger in them and spinning. They should rotate smoothly and easily, without any gritty feeling. If they feel gritty, it's time to replace them before riding again.
The valve stem itself is also something you should inspect. Bend it and look for cracks anywhere in the surface, but mostly right where it gets narrow to go back through the rim. It's easy to change right now, and more work if it fails when you don't need to change the tire. Valve stems are removed by cutting them off with a utility knife. The "tool" to install new ones is a couple bucks at auto parts places. It screws onto the threaded part of the stem and gives you something to grasp so you can pull it into place. You put the threaded part through the hole, attach the tool, and pull it into place.
Here's an example of a valve tool from Aerostich. It both removes the core and screws onto the valve stem to pull it through the rim.
Get the shortest stem you can find. Angled ones are a bad idea (need to be replaced more often) and the screw-together metal stems can be a PITA to get to fit correctly, and to remove later when they eventually fail. It's best to just change the valve stem every 3 or 4 sets of tires. The stem is the same standard size as those used by cars. You should be able to get one at any tire retailer. They may just give it to you. Tireflies and other heavy caps will lead to premature stem failure. If you run anything but plastic caps, you'll likely be doing valve stem replacements a lot sooner.
It's important to note that tires are directional, due to how they're constructed. The arrow is plainly shown on the side of the tire, like this (to the left):
Also notice the DOT code. It's a 4-digit code that lists the week and the year the tire was made. This one is 3205, so the 32nd week of 2005. More than 3 or 4 years old and tires start to go 'off', get hard, and aren't any fun to ride on (worse than the stock Dunrocks on the 250).
Finding the wheel's heavy point
Before you put the tire on the rim, you need to find the wheel's heavy point. You only need to do this once for the lifetime of each wheel. Go to How can I balance the tires by myself? and do that part now. It will also tell you how to use the factory's paint mark to find the correct point to mount the tire on the wheel.
Mounting the new tire
Make sure you have read the balancing article and put the "light point" mark on the tire at the heavy point of the wheel.
When it comes time to put the new tire on, you should be able to just walk the first bead over the rim without any tools other than your body weight. If needed, you can use a rim protector, tire lube, and tire iron to help, as was needed here:
Then, push the first bead into the center of the rim, put some lube (see Hints & Tips) on the bead that is still outside the rim, and slowly work the tire on with your irons. It is important that you put the bead that is already all the way on the rim into the center of the rim (the deepest part), and not against the side of the rim on the far side. This will give your tire more slack, and will make it less likely that you'll have to bust your fingers trying to get the second bead on.
Keep your knees on the part that's already on the rim and the first bead in the low center part of the rim. Work your way around with your tire irons, and it should only be difficult the last little bit.
With the tire on the rim, it's time to seat the bead with an air compressor. Those cheaper units that just provide an on-demand supply (often in blue boxes at gas stations) do NOT have enough oomph to do the job. You need a good source of air, but that's usually easy to get ahold of at any sort of shop doing any sort of work, or the old time gas station/garage. They always have good air.
Fill the tire up without the valve stem core in the valve stem, and listen for 2 "pops". Front tires are usually very quick and easy with this; rears can be more difficult. If you have trouble, just lay the tire on the ground, as it was when you were changing it, and use your spare hand and knees to bump and lift the tire where air seems to be escaping from. It will seat with some patience and work. There have been members who have managed to seat the bead with tire lube and a high-pressure bicycle pump. YMMV
If you have a problem seating the bead, wet your hand with plain old water or tire lube and rub it (just a bit, you don't need to soak it) around the area not seating, and it should pop right out.
One tip, if the above methods don't work, is to use a ratcheting tiedown wrapped all the way around (not across) the tire and compress the tire down into the rim (this will force the beads towards the lips). Then you can seat the beads with air, as usual.
A variation of this is the rope-and-a-stick trick, shown below. Basically, you make a tourniquet around the circumference of the tire to try and encourage the sidewalls to splay before adding air.
Once the bead seems to be seated, look for an even ring on the tire all the way around the rim. There are usually some rings molded into the tire to make this task simple. There should be an even distance between the ring and the rim all the way around. If it's not even all the way around, the bead is not fully seated.
Now, put the core back in the valve stem and fill the tire up.
Balancing the wheels is an important part of mounting your tires and should not be neglected. It's so important, we've made a separate article for it. Follow this link and balance your tires now:
Reattaching the wheel
After you've balanced the wheel, you're done mounting and balancing. Time to put the wheels back on the bike and go for a ride.
Reinstall the wheel:
Be sure to use a new cotter pin. Be sure to reattach the brake and use the proper torque on everything.
In-depth article from clarity.net
This one is on a tubed tire. It's slightly different. Also, he obviously doesn't care what his rims look like...