Place masking tape over the drain to keep out debris when you're ready to work. Place a canvas drop cloth over the floor of the tub or shower to protect the surface from the sand-like grout that can scratch it. If you're dealing with a bathroom where the wall grout has completely broken down, you'll first need to remove the tub spout, faucet spout, handles and trim. If you're just spot repairing, you can jump in and start extracting grout.
If the tub spout screws off, twist it either by hand or with groove-joint pliers padded with tape to prevent marring the spout finish. If you have the type that slips over a copper nipple, use an Allen wrench to loosen the setscrew on the underside to twist-pull the spout off.
If the spout is stuck on, try inserting the blade of a large screwdriver or the handle of a pair of pliers into the spout opening to twist.
To remove faucet handles, first use a nail file or knife to pop off any decorative cap that covers the handle screw. Then, remove the screw with a Phillips head screwdriver and pull the handle straight out. With the handles off you can remove the trim by hand. First, unscrew the stem nipple (a cylindrical sleeve) from the valve and either unscrew or pull off the escutcheon (the flange that hides the rough hole in the tile). To free the escutcheon, you may need to score any caulk between it and the tile with a utility knife.