How often should you change engine oil on a 1998 Honda Shadow 750?

This depends on the state of the engine, up to a point. If you are still running the original engine, I would change the oil and filter every 2-3 thousand kilometres. If your engine has been rebuilt with new parts, then you can use the engine oil for a bit longer, but do not exceed 4-5 thousand km. Be sure to use JASO-MA or MA2 approved oil only and not ordinary automotive oil as the latter will damage the wet clutch.