Can you hear the motor running when the drum should be turning? If so, then it's probably just the drive belt needs replacing, which is a fairly simple DIY job on most machines.
If the motor isn't running, it could be any one of a number of things, from worn brushes, to burned out windings, to a faulty controller unit, to a loose connection.
Whenever we have to fix the washer, it's the brushes. I have no idea what that means,
You have to get power to the coils which are on the rotor, which obviously isn't as simple as just running wires to them since the whole rotor needs to spin round! The way it's done is to mount metal slip-rings around the shaft, then the brushes ride on the rings under spring pressure to provide the electrical connection. The brushes are normally carbon-based little blocks, which wear down over time.