The best way to get speed skills is on the expressway in the northern part of the map. Just start at one end and go to the other. if you haven't gotten all 20 speed skills by the end, then run it back the other way. Usually just 2 runs is all it takes.
The important thing is that these must be "Speed" skills and not "Great", "Awesome", "Ultimate", etc. To get a speed skill just keep your speed steady between 120 and 140 MPH. If you hit 150 you will start earning "Great" speed skills, which won't count. If you go under 100 you won't earn any.
Driving at these speeds is pretty easy already, but picking a C class car might make it easier for some because it is no trouble to keep the speed down.