When does the USAV season start and stop?

This depends by region as the season usually starts with a "friendlies" set of tournaments before going into the true tournaments, Regionals and Nationals.

Friendlies are, basically, tournaments that are run by USAV clubs for USAV teams, but people are not required to be dedicated to an individual team.  This means that a player hasn't picked which team they're going to be playing for during the rest of the season.  They are tournaments where you can "test" the waters, as it were.  In the LoneStar region, friendlies for 2009/2010 were in September and October.

Starting in November, for the LoneStar region, players have to commit to an individual team.  Some regions have different timeframes. The Rocky Mountain region, for example, doesn't require players to commit to an individual team until about January.  

In March/April, there's usually a major tournament. This tournament, dubbed "Regionals", is held to qualify teams for Nationals and for the prestige of being 1st or 2nd in the region.  Officially, only the first place team is "guaranteed" a slot in the Nationals tournament. 

In May/June, there's a single Nationals tournament.  This tournament is held in a different city each year. It's been held in places such as Austin, Minneapolis/St. Paul and (this year) Phoenix.  Teams from all over the nation come to compete against others and see how they do.  There are usually 50+ teams in many of the divisions and the tournament lasts four days.  As I said, only the first place team for Regionals is guaranteed a slot. That having been said, there are usually many more slots than there are teams so if your team wants to go, you don't have to place at Regionals.