Thank you for your question. The number of players on the team varies, but is typically between 13 - 15 players. This is due to having multiple pitchers, the ability to play multiple games in a day (tournaments or doubleheaders)or in case of injuries.
However, I believe that your real question is how many players are on the field at a time. In most cases, there are nine players on the field for fastpitch softball, covering your standard positions. I have seen, in the 10U age bracket and younger, cases where there where 10 players on the field at a time. The additional player typically plays either a short outfield position or plays as a fourth outfielder (left center and right center).
Note that is for the fielding side. You should note, however, that in some cases, you can actually have more than 9 players in the line-up, when still playing only 9 players in the field. This happens when one of your players is the "designated hitter" for one of the fielding players. In this case, there are actually 10 in the game, with 9 players in the field, and 9 players hitting (just not the same 9). The "designated player" rule is similar, but with slightly different outcomes. Read the softball positions page for a more complete explanantion.
Oh, and one more thing: You can generally have a runner for your pitcher and catcher. This is called a courtesy runner, and is meant to save the strength of your pitcher and allow your catcher to go back and get her gear on so as to keep the game moving.
Hopefully, this explains it. Baseline, 9 players at a time (with possible exception to 10 at the younger ages), with a few exceptions for DH and DP.