Is all that's needed to backup a wallet a copy of the wallet.dat file? And to restore it to a new machine do you just install bitcoin again and copy the wallet.dat back?
Yes.
Also, what would happen if you put the same wallet.dat on 2 machines at once?
(Those questions were probably answered elsewhere but I never have any luck finding answers)
I didn't try to do it. I think it's most likely the client (and you) will get confused because the history and balance will change if the other copy spends some coins. After the first outgoing transaction, there will also be new private keys for that copy of the wallet, so the two wallets will no longer be identical and it will be difficult to merge them again. Better to avoid doing it.
