After you choose the type of bike tire that you're looking for, you need to make sure that it will fit on your bike. Picking the right size tire comes with two main areas of measurement. Width and Diameter. Finding that goldilocks perfect tire can take some experimentation and testing as well as some soul searching to find out exactly what it is you're trying to get out of your riding experience.
The diameter is pretty simple - it's the size of your wheels. If you're a mountain biker, you're looking for 26", 27.5" or 29". Nearly all modern road bikes are 700c, which is actually the same as 29". If you've rocking a vintage European steelie to go along with your vest and handlebar mustache and hipster attitude, it's possible that it's another esoteric old size. One surefire way to get the right size bike tire is to check out the spec on the side of the rim and/or the old tire to understand what diameter you're working with. Diameter is not a preference, either it fits the wheel or it doesn't.
Choosing the right width bike tire can be a little more tricky. Unfortunately, inconsistencies between the tire manufacturers can make this more difficult because apparently 2" doesn't mean the same thing in Kenda as it does in Maxxis or Continental. A quick work around is to look at the stock brand/spec of tires for the bike or fork you're looking to get the tire for and use it as a baseline. Keep in mind that you need space to allow for wheel and frame flex, fenders, mud clearance and possible woodland creature clearance. If you're running a road bike with caliper brakes, you'll make sure you're clearing your stoppers as well.
Tire width also affects performance as it changes the size of the contact patch with the ground as well as the overall volume of the tire. The larger the tire is, the lower pressure you operate at and can keep the rim from banging on the ground, meaning more traction. This affects cornering, rolling resistance and overall traction as well as riding comfort. The tradeoff is generally in efficiency - fatter tires are going to be heavier and roll slower at a given pressure than thinner tires.
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