I have to re-grout - as in REMOVE - my bathroom tile, since it is so old. How do I go about doing that?
If you want to REMOVE the tile from the wall you can use a hammer and a flat bar or a wide flooring chisel. If the tile is mud set (set in a cement base you'll need a pair of tin snips to cut the wire with or you can break the wire with the claw of the hammer.
If you want to REGROUT the existing tile, purchase a grout saw, and saw the grout from the joints. After cleaning the joints, mix the grout rather thickly, force into the joints at 45 degrees to the joints, remove the excess at 45 degress to the joints with a "grouting sponge trowel, wait, tool the joints (to compact the grout) usintg a suitable tool, then rinse with a sponge (time and time again), then when the surface hazes, polish with a clean cloth.