If the saddle is high enough to give you good leg extension for power, you shouldn't be able to touch the ground. (maybe with a teeny tippy toe, but that's about it)

Watch some other people riding. You'll see that they use one of their pedals like a step-stool to raise and lower themselves to and from the saddle.

Best way to learn would be to have your fitter teach you, because written descriptions just don't do it justice. It's a sweet, elegant move.

Until you learn that move, it might be safer to switch to platform pedals. In that case, you can really wear just about any shoe you like.