How do women with frozen eggs conceive the children if they use the eggs?

It has to be IVF.

You pretty much have to use IVF with frozen eggs. It's a delicate process.

I don't think so. The time window is very small.

A viable egg lives less than a day. Why, after going to all the trouble to have your eggs harvested and stored outside the womb, would you suddenly decide to leave it up to mother nature? Why not continue with medical intervention? Is the goal to have a baby, or be natural?

And why would anyone want to have sex right after the procedure (whatever that might conceivably be) to put an egg back into a fallopian tube?

Could you? sure.
But remember, that just because an egg and sperm are in the same vicinity doesn't mean they are going to get together. If they click, they still have a lot of work to do to start the pregnancy process. Add to that, that many eggs won't be viable when they unfreeze, it's far from a surefire method.