Tires are tricky business but the first thing to remember is that each number means something. My tires are P265/65R17. You can determine what kind of tires are on your car by looking at the tire itself or (more easily) by going to a tire distributer's webpage and entering the details of your car.
For more help, about.com has this wonderful illustration showing where you can get all the numbers from:
The "P" means a passenger tire. These tires are usually softer for a smoother ride. A tire with "LT" is a light truck tire and somewhere on the tire it will say the load capacity. If you have a "LT" tire, you need to also take into consideration how much weight you're going to be pulling.
The "265" is the width of the tire (in millimeters) from sidewall to sidewall. The larger the number, the wider the tire.
The "65" is the tire's ratio of height to width. This number is also indicative of the tire's purpose. Numbers lower than "70" have better steering and handling because of the shorter sidewall.
The "R" means that it's a radial tire. If your tire was purchased in the last few decades, it's a radial tire.
The "17" is the rim diameter measured in inches.
Sometimes these numbers are followed by a two digit number and letter (like "89V"). This number is part of a code which tells you the load capacity. Remember the number is per tire, so if you want the maximum capacity for the car, you'll have to multiply the number by four. The letter tells you the maximum speed the tire was designed to run for extended periods of time.
For the maximum load capacity per tire, you can check a table located on any number of websites including: http://en.wikipedia.org/wiki/Tire_code
Here is a list of the tire speed codes:
S 112 mph
T 118 mph
U 124 mph
H 130 mph
V 149 mph
W 168 mph
Y 186 mph
Once you know what kind of tire you have, you can compare tires by using the Uniform Tire Quality Grading Standards (UTQGS) ratings. UTQGS ratings are based on three categories: treadwear, temperature, and traction.
Treadwear is rated on a scale of 20 to 620. In general, the higher the number in treadwear, the better the tread. A tread rating of 200 will last twice as long as a tread rating of 100. In my short research experience, I would consider tread ratings in the 500-600 area as good. You should be aware that tread ratings were too expensive to be done by the government, so each tire manufacturer determines their own tread ratings and then justifies its rating to the government. This means that you're not necessarily comparing apples to apples when comparing different brands, but it does help.
Temperature is graded in the form of A, B, C (with A being the highest). This represents the tire's resistence to the generation of heat.
Traction is graded in the form of AA, A, B, and C (with AA being the highest). This represents the tire's ability to stop on wet pavement. It does not take into consideration acceleration, hydroplaning, or cornering.
