Removing ceramic tile is usually a nightmare for most homeowners, as it is a thorough job and it takes quite a lot of time and precision.
However, whether it is a nighmare or not depends very much on the surface on which they are installed, as well as if you have to remove just some tiles, or all of them. Completely removing ceramic tile will be easier, because you won't have to worry about damaging the rest of the tiles. Removing just some tiles will require much more care, as you have to be careful not to damage the other tiles around the ones being replaced.
Start by removing the old grout from around the damaged tile, using a chisel or an awl. Do this carefully, so as not to damage the surrounding tile. After removing the grout, chip out slowly the old tile, by breaking one small piece at a time with a hammer and chisel. It will take some time, but if you want to do the job right, you need to be thorough. Once the old grout and tile are removed, scrape them carefully off the floor, until the surface remains clean and smooth for the new tile to stay in place. Removing ceramic tile must be done carefully, don't try to remove more tiles at once. Each of the tiles must be removed from the floor (or wall) one by one. Be very careful not to damage the surface beneath, as it will provide a base for the replacing tiles.
If the tile is set in adhesive or well adhered to the mortar, removing ceramic tile will be quite a challenge. Still, it's not impossible. For a faster and easier job, you can use a carbide drill bit, with a 1/4" to 1/2" diameter. Drill some holes in the tile, so as to make them easier to break apart. After drilling the holes in the tile, use a chisel or a screwdriver to pry out the rest of the tile.
Also, removing ceramic tile might be easier if you start at the doorway and work your way across the room to the opposite side. This will allow a convenient progression, and many of the tiles will be slightly loosened when you remove the tiles around them. Basically, the hardest part of removing ceramic tile is actually prying the tiles from the base and adhesive.
Once you have removed all tiles that needed replacing, all you have left to do is to clean up the area. Sweep the entire room to remove all the tiles and tile chips, as well as all the dust created in the process. To remove the last traces of dust, use a mop or a damp cloth and wipe the newly exposed surfaces.
For a large area, removing ceramic tile shouldn't take more than three days of working at a moderate pace. And to be honest, the whole process of removing ceramic tile is more annoying than difficult, because you have to be so thorough and careful. Still, when you think of all the money you'd pay a professional to do the job, three days of reoving ceramic tile on your own might just be a very small price to pay.