Chisel out the old tile. Chip out the grout first. Wedge the chisel under the edge of the tile to pry it loose.
Sand down the surface after you remove the tile, so that you have a smooth area to work. Use a grinder chip away the material and then a sander to finish it up. If you don't want to go to the trouble of making the surface smooth, you can spread thinset over the surface and smooth it out. Let the substance dry for 24 hours.
Attach a wooden strip the width of the fireplace that is to be tiled to create a bottom edge of the upper section of the fireplace. Screw it into place. Keep a level on it as you attach it to ensure that it stays horizontal.
Measure the width of the fireplace to determine the mid point. Draw a line up the center of the fireplace at the midpoint. This will keep the pattern of the tiles symmetrical.
Spread thinset on the fireplace just above the wooden strip. Run the ridged edge of the trowel through it to create lines in the thinset. Don't spread on more than a few tiles worth, so that it doesn't dry out while you are working.
Determine the pattern you want for you tile, which is typically staggered or one on top of the other. For staggered tiles, set the first tile so that the center of it is on the center line that you drew. For stacked tiles, set it so that the left edge of the tile is just to the right side of the center line.
Place the rest of the tiles in the row to the left and right of the first tile. Press the tiles slightly into the thinset. Check the tiles with a level every once in a while to ensure they are straight. Place spacers between the tiles to keep them from sliding too close. Repeat the process with the rest of the rows above the first, stacking them as you want them.
Remove the wood strip once the top is done. Apply tile down the sides of the fireplace. Let the tile dry overnight.
Spread grout over the tiles with a grout float. Press in so that you work the grout in between the tiles.
Allow the grout to dry until it is firm to touch. Wipe with a damp sponge to remove the surface grit. Leave the grout to dry overnight.