Step 1: Supplies!
A stuck wood screw - in this case a smallish, thinnish, bronze slotted flathead screw.
A length of steel rod matching the size of the screw head - I used a 20d nail.
A propane torch.
Vise-grips - 'cause your gonna make that nail HOT.
A screwdriver that fits the screw well.
Step 2: Make Some Hot Metal.
Heat the end of the rod cherry red.
Step 3: Heat the Screw.
This softens the wood fibers around the screw and also breaks any glue bond.