Question

How does dark energy affect the expansion of the universe?

Answer 1

It accelarates it.

Explanation:

That's exactly how we found it. We measured by Hubble-diagram that the Universe's expansion is accelerating.
Since gravity between normal objects is attracting, there is nothing what could explain this. So we assume that there's something else, some kind of dark energy, what we don't know anything about, just that it's accelerating expansion.