To replace a broken tile you remove the grout surrounding it with a grout saw, break up the tile with a hammer, or hammer and chisel, then replace it using thinset. Then grout.
Matching the tile and grout may be your biggest challenge.
But before you replace the tile, you want to fix the reason for the crack, otherwise it will more than likely happen again.
A pic would help.
Also, where is the tile? Floor, wall, shower, etc.?