Much depends on why the screw snapped in the first place.
It's often the case that the screw sockets are misaligned (through overtightening the screw, due to a poorly fitting crook tenon), which it turn cause the screw to bend...which in turn causes it to break.
In this case the remainind stub of thread should come out easily enough provided you can get something to grip and turn it.
If the screw snapped because the thread itself is damaged then it's going to be a much more complicated job.
The simplest DIY approach is to try to drill the stub out, but you run the risk of any drill bits (or easy-outs) slipping and chewing up the sockets.
So, find a piece of plastic tube that will fit inside the unthreaded socket. Windsdcreen washer tubing is often a good bet, but you might also find that a Rawlplug (used for fixing screws into walls) will do.
Poke this into the unthreaded socket, then feed a drill through the centre of the tube.
The tube doesn't have to be an exact fit in the socket, but the better the fit the less likely it is that the drill bit will wander off-centre as you drill. The drill bit though should be more or less an exact fit to the hole in the tube.
You'll still need to be careful to keep the drill level, but the tube will both roughly centre the drill bit and prevent it slipping off the stub and chewing up the socket walls.
Use a cordless drill on a low speed...you'll probably find that once the drill 'bites' it will spin out the stub.
If this doesn't happen after you've gone some way in then it's quite likely that the stub will have to be drilled right through - though at this point you could insert an easy-out and 'reverse' the stub out.
This is when you will have to decide whether to carry on or take it to a tech...as it's around this time when things can go badly wrong.
Regards,