2007 harley davidson xl sportster 883 speedometer is not working. How do I troubleshoot this problem?

If you're lucky it might be the speed sensor located in the gearbox casing. This is a hall effect device and is magnetic and so can pick up metal fragments from the inside of the gearbox. I have a 2001 Sportster and the Sensor is located on the top of the gearbox casing, just below the starter. I'd expect it to be in a similar position on a later bike such as yours, but I can't be sure. Once you've located it, take it out (can be a bit fiddly) and make sure that its clear of any debris. If not the sensor, you're probably going to need to substitute in a working speedo. Be careful because a pre-2004 speedo is electronic, but is not compatible with 2007 bike. Best of luck!