Is the wheel secured with nuts, a skewer, or something else?
Nuts need a spanner. A skewer is usually quick-release (lever cam) but may need an allen key. There may even be Allen key bolts but less likely. Some QRs have a lever that can be removed for security, these aren't very common either.
If the bike has rear-facing drop-outs there is probably another bolt you need to undo; this is the case for most fixed-gear bikes, some single-speeds and bikes with hub gears. (E.g. Sturmey-Archer 3 speed.)
Webstes such as Sheldon Brown and Park Tools have useful instructions on how to do most things to most types of bikes.