How do you fix non working speedometer?

If the speedometer is an older, analog style, then the most common cause is a binding or damaged speedometer cable, which runs off the tail end of the transmission. You can remove the speedometer cluster and check if the cable on the back is connected or is visibly damaged. Worst case scenario would be the actual mechanism that drives the speedometer is damaged; the mechanism on most cars is not serviceable and you would have to replace the entire cluster.

On some newer, analog speedometers, there is no cable. There is a signal wire that makes the needle move. With this type, they are usually computer controlled (especially if they have a digital odometer), and it would be best to seek the advise of a professional before attempting service.

If it is an older digital gauge set, used in the '80's and '90's, then it might have an issue with the speedometer cable. But if there is no reading on the speedometer (not even a 00mph), then the problem is more than likely the digital display. The first thing you can try is finding the power and ground connectors to the display, and ensuring that they are connected. If it is getting power and ground, and there still is no display, then the cluster is faulty and needs to be replaced. I've heard of people rebuilding digital gauge cluster, with mixed results.