To fix a broken ceramic tile, make sure the replacement piece (or the original piece, if still in good condition) fits perfectly in the space or gap created by the break, lather the back of the piece with the selected grout or grout/adhesive compound, and fit it into the gap. Allow the piece to dry overnight.
Before adding adhesive, clean the site of the break as effectively as possible. If the repair involves an area close to the edge of the tile, sand away as much of the original grout as possible using a grout saw. Additionally, if smaller broken pieces still remain, remove them gently using a 1/2-inch cold chisel. Make sure to angle the chisel so as not to damage any drywall behind the tiling.
To hold the replacement piece in place while the adhesive dries, apply a quality tape product across the surface. Use only grouts and grout/adhesive compounds designed specifically for ceramic, or the results turn out shoddy. To confirm that the new grout or adhesive compound matches the original colors, apply it to a piece of cardboard the night before the repair, and allow it to dry overnight. Compare the two results the following morning.