Sure you can spend $30 on a ready made cleaner to be used with a power drill, but half the fun of homebrewing is tinkering with your setup.
Step 1: Material and Tools
3/8" aluminum rod roughly 3' long
#8 pan head screw
#8 acorn nut
Washable mop head( I used a Libman)
Drill bit (3/16")
7/16" combination wrench
Step 2: Disassembling the Mop Head
There is a square plunger and base which is pressed into the plastic connector of the mop. Using a pair of side cutters you can trim away bits of plastic to help remove the plunger.
Step 3: Modifying the Aluminum Rod
I also debarred the holes, but this is not required.
Step 4: Assembling the Cleaner
Assemble the cleaner using the #8 screw and nylon washers to help prevent tearing of the cloth strips. Two strips folded in half should used on each side of the aluminum rod. Finally add the remaining two cloth strips, nylon washer and acorn nut and tighten.
For $12 in materials and 20 minutes it works great.