I am going to regrout the tile in the bath/shower area. What is the easiest way to remove the old grout?
A rotary tool (e.g. Dremel) with a grout removal bit:
An oscillating multi-tool with a grout bit:
A grout saw:
Dr. Pickems approach:
Ok... this question asked easiest. (And also a method that I have successfully used).
Get a good quality breathing mask, stainless steel wire brush, some gloves and some pool acid (Hydrochloric Acid)
If you have normal tiles (porcelain or ceramic) you can simply pour the acid onto the shower floor... will eat away the grout in no time. I would also use small amounts at a time so that you are not overwhelmed by the noxious gasses.
Please ensure that you have made your bathroom well ventilated at all times.
Wash away the small portion of acid with water after every application.