The fountain plays in the evening until midnight I believe. There are signs posted by the fountain for when the shows start and the speakers announce when the next show is.
This is a must see if you go to Vegas. It is completely free and I recommend watching a show from the right side if possible because that is the main part of the fountain. They do many different songs and the choreography follows each song so every show is different.
Watching a show a something quick and nice to do every every night.