To my knowledge its impossible to remove without breaking it up. Take a hammer and lightly tap, chisel out all grout / mortar that remains so that area is clean. Then mortar, lay new tile, grout, seal.
But if you think it's completely detached from te mortar underneath, you can delicately chisel out the grout lines and try to pry up the tile. You will still have to remove all the old mortar and then follow instructions I put above.
I agree with Krys. We recently had to remove a couple tiles when we bought a new dishwasher as they are just enough taller now that we couldn't install it without removing a couple tiles. It was a bit time consuming, but you'd never know now they'd been removed and replaced.
It depends where it is in the kitchen ?. If you have never done grouting before , You shouldn't touch, hire a professional to come and replace it.
Does the tile need to be completely replaced or do you think you can repair the tile without having to replace it. If you think you can repair it without replacing it, you may want to read this article from our DIY section from remodeling home improvement magazine.
Check out this article on this