Hi, Keith. UL doesn't "approve" anything anymore. You can obtain UL listing, which means your product can carry the UL certification label. It shows that samples of the product have been tested by UL and been found to conform to the applicable standards (available, of course, from UL).
Without knowing more about your product, it's not possible to say which standards you must test.
You might want to go explore the UL website. They do have quite a bit of non-technical information about their standards, which will give you an idea where you want to go.
But UL listing isn't cheap, and it's an impossible project for a newbie. If your product is worth it, and UL listing is essential, you should hire an engineer with some experience in the applicable standards and the UL submittal process as a consultant. He can help to guide your product through certification.
Good luck Chris