Jira natively doesn't log this activity in 6.1 or below. Some tracking is implemented in 6.2 (I've only glanced at it so far, so I can't tell you how comprehensive it is. Looks like it covers a lot though).
So, if you're not on 6.2 (i.e. OnDemand), you're probably stuck. You can do things like ploughing through access logs, but that won't tell you everything, and probably won't have full details of what they've done. There's also a plugin which can do this tracking (v4+), but it only works from the point at which you install it.
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