Master: We use 'troubleshooting' instructions provided by mfg. Also, a known 'good bulb' & a digital voltmeter for output and cap testing. THe ballast mfg sites have troubleshooting suggestions, and output info available. (Advance; Universal; Valmont, etc)
I use the known good lamp approach. First change the lamp, if that's not the problem, replace the ballast. On HID, since most ballasts come as a ballast kit, replace all the components. There are lamp testers available and I have one but rarely use it. This saves a lot of time and IMO money, since I don't have to go back a few weeks after I've changed the capacitor in a fixture to change the igniter.