How is the universe expanding?

Since then, the universe's expansion has mostly slowed down because gravity is the only long-range force that is known to always be attractive.

Evidence from more recent research (Perlmutter et al., 1998) indicates that the expansion may have been accelerating more recently as a result of dark energy's ability to overcome gravity.

This is "like dark matter, but significantly less well understood," according to a highly entertaining physicist (we seem to have no clue whatsoever about dark matter.)

The universe is expanding uniformly in all directions, as observed by the observation that galaxies are moving away from one another, and that the more distant a galaxy is from the observer, a phenomenon described by Hubble's law, which states that the velocity of recession of a galaxy is directly proportional to its distance from the observer. The Big Bang theory, which holds that the universe started as a hot, dense state some 13.8 billion years ago, is the most widely accepted explanation for this expansion. The theory also states that the expansion is not caused by galaxies moving through space, but rather the expansion of space itself is carrying galaxies with it.