Why does your motor make a tapping noise when you first start your car and after it has run for a while is it valve tap and how can you fix it?

There could be various reasons for the tapping. My first inclination would be to check the oil dipstick level and be certain that the oil has been changed. Worn out dirty oil will wear out a motor fast. You could need the valves adjusted or something replaced in the valve train. However, it could be something more serious. If it is louder than just a mere tapping, I would say that you possibly have a rod knocking. If you catch this early enough, then it could be fixed by a mechanic with a few parts. If you wait too long, then the rod could eventually eat through your engine wall. The only safe way to fix that would be to replace the engine block or the whole engine.