How do I(John Goskusky)maky a500 watt power inverter?

Question

in electronic discrete parts

Answer 1

Fundamentally, you study electrical engineering for several years and burn up a few trial inverters along the way.
Since you've only mentioned a 500 W device, I will presume that you want to convert 12 Vdc (from an auto) to 120 Vac, 60 Hz, single phase. You will need an oscillator, a 4-IGBT module, microcontroller, sensors, and a lot of other interface electronics. If you don't wish to use IGBTs, you could also use SCRs or GTOs, but they become more complicated....
Another way would be to build a back-to-back DC motor to AC generator, but these would be overkill for 500 W.
If you really want to learn, there are plenty of online and print references, especially application notes of electronics manufacturers, like TI, International Rectifier, Infineon, etc.
If you just want an inverter for your auto, go buy a retail one.

Answer 2

If you have to ask here, go buy one before you kill yourself or someone else.