To determine the speed rating on a set of tires, look for it on the sidewall. It is usually located near the inner part of the tire and is included with the load rating. For example, it may say "95H," with H being the speed rating.
Speed ratings follow a standardized naming practice, so the letter corresponds to how much speed the tires can safely handle. In general, B is the lowest speed, while Z is the highest, with the ratings progressing in alphabetical order. H is a common exception and is rated for fairly high speeds, perhaps because it once stood for "high performance." Speed ratings are described as being "up to" a certain speed, which means they should not be driven faster than that. For example, H tires are rated up to 130 miles per hour.
The load index and speed rating are typically located near the temperature grade and maximum pressure rating. Some older tires place it in other locations, such as near the R symbol, which signifies radial construction. Some tires do not have the rating on the sidewall. For these tires, you can take the tire into a tire shop or try to look it up online at the manufacturer's website. However, speed ratings are required on most tires manufactured since 1991. Unless dealing with specialty tires, reading the sidewall is probably sufficient.