This is a common problem with my partners bike. The first time she needed something tightening but I just can't remember what it was :-( The LBS did it in 2 minutes.
Since then she's had an improperley seated wheel (took it out and put it back in and it was fine), loose spokes (spoke spanner fixes that fairly easily) and a broken axle (if you removed the wheel you could tilt the axle while holding the bike and see inside - the LBS fixed that as well).
I'm far from an expert but what I have learnt is:
Does the wheel wobble when you push it side-to-side (not spinning it)? If so it might be the axle or that thingy needing tightening and either way I should take it to the LBS as I don't have the right tools.
If it only wobbles when spinning then has the wheel been unseated since it didn't wobble? If so make sure it is seated properly.
If the wheel is seated properly you probably have some loose spokes. You need a spoke spanner, a texta and Google :-)