A loose tile in a shower is a relatively easy fix -- all you have to do is fully remove it, clean up the space and reinstall the old tile or a new one. But it's not something you should take lightly or put off. A loose tile will allow moisture to get into the substrate material. This could potentially cause the rest of your tiles to loosen, and you might be faced with replacing the entire floor, which isn't such an easy fix. Address the problem as soon as you discover it, and don't use the shower until it's finished.
If the tile comes completely out by hand, remove it. If it's still partly adhered, use your grout saw to dig out the grout surrounding the loose tile. Once you've got as much of the grout removed as you can, use your hammer and chisel to gently tap at the bottom of the tile, where it meets the subfloor material, and work it until it comes out. Continue using the hammer and chisel to clean up the space left by the tile, loosening up all the remaining grout and mortar. Vacuum up the debris. Use your detail sander and 60-grit paper to sand away the last of the residue. Vacuum that up as well.
If the old tile is still in one piece, in good condition and not cracked, clean it up with water and a scrub brush. If the tile isn't salvageable, bring in a new one of the same kind. Use your putty knife to spread thinset mortar on the back of the tile, covering it completely with a layer about 3 mm (1/8 inch t)hick. Press the tile firmly into place in the space left by the old tile. Use the edge of your putty knife to scoop out any excess mortar that seeps into the grout line around the tile. Use your sponge to wipe off any excess mortar from the face of the tiles. Let it set overnight.
With your putty knife, scoop your pre-mixed grout out of the container and press it into to space around the tile. Use your damp sponge to wipe off excess grout from the tile face and smooth out the grout in the lines, getting it to the same level as the surrounding grout. Let it set for two days. Use a small brush to apply grout sealer over the new grout.
If additional tiles around the loose one are going to have to be re-mortared, now's the time. After the loose tile is out, press on the surrounding tiles while watching where the bottoms meet the subfloor, and see if there's any movement there. If so, remove and reinstall those tiles as well.
Wear eye protection when using your grout saw, chisel and sander.