Go to the hardware store and examine similar ones. Common faucets are screwed onto a stub out pipe. Scrape away the caulk, if any. Wrap the faucet in an old towel and try to rotate it by hand counter-clockwise. If it is on too tight, use a pipe wrench, perhaps hooking onto the faucet outlet or other convenient point. When turning, try your best to not exert a bending force on the faucet (parallel to the wall), just rotate it. Chances are when it was installed there was a small gap between the faucet body and the tile, which was then sealed with caulk, so you aren't applying force directly on the tile. It will come off. If you end up damaging it, just replace it, they aren't expensive.
Go to the hardware store and examine similar ones. Common faucets are screwed onto a stub out pipe. Scrape away the caulk, if any. Wrap the faucet in an old towel and try to rotate it by hand counter-clockwise. If it is on too tight, use a pipe wrench, perhaps hooking onto the faucet outlet or other convenient point. When turning, try your best to not exert a bending force on the faucet (parallel to the wall), just rotate it. Chances are when it was installed there was a small gap between the faucet body and the tile, which was then sealed with caulk, so you aren't applying force directly on the tile. It will come off. If you end up damaging it, just replace it, they aren't expensive.