Not a lot. Occasionally they put pressure on members who are seen to be misbehaving: Nigeria was recently threatened with expulsion over its civil rights record, and pressure put on Pakistan and India over the build of tensions over Kashmir.
Do member nations get together from time to time?
Yes, there are "commonwealth conferences" of the heads of states of member nations. There is also the "Commonwealth Games", a mini-Olympics for member states, which also encompasses sports such as bowls and cricket. Naturally, Australia always win everything :)
Note to all who might be confused by the move to "The Commonwealth": check out http://www.thecommonwealth.org, "The Commonwealth" is the correct name these days, not "British Commonwealth" or "Commonwealth of Nations". --Robert Merkel