A lot depends on how many are in the room and if the person who is (nominally) in charge knows everybody and what sort of stuff they are likely to do. But the only fair way is to go around the room and let everyone take their turn. Some people won't 'just jump in' and prefer to be invited (that's not me of course!).

In the meantime, to everyone who attends singarounds or whatever you have in your neck of the woods, it is useful to bear in mind what has gone on just before. It's best to have two or three alternatives ready for when it comes to your turn. Or if that's not possible, just ask the person organising if he or she wouldn't mind coming back to you later if you think that your next rendition won't fit too well with what's gone just before.

I know - I was that melodeon player!

Les