!!!! Be careful !!!!!

You MUST drive an LCD with an alternating voltage (DC current must be zero), otherwise permanent damage to LCD may occour. So you must toggle the driver outputs and the backplane if you're implementing a software LCD driver an output port. Multiplex 2:1 is very easy to implement using the method Craig described, but 3:1 or 4:1 is not so easy. Then you'd better to use an LCD driver - there are many available.

I have been doing so once using PIC 16C54.