There isn't a speedo in the game, so you just have to go for it.
Easily achieved in either a police car or a Kamara. If you're further into the game and don't mind the handling, the hot rod is an obvious choice too.
Just find a nice long stretch of road and floor it! I find the west to east run along the upper-most island on the top left of the map the easiest spot to get up to speed. Alternatively, you can get yourself a fast run up to a stunt jump - when going at speed, you get a little boost off the end of the ramp to increase your chances of making the jump. According to my stats, my speed record went up to 184mph after the stunt jump over the lake to the Beanz Coffee Shop.
Edit: That's now at 195mph after doing the central lake stunt jump in a Kamara.