Drilling into tile is easy if you have the right tools. It took me a little--a lot--of trial and error to figure it out. Do NOT drill into tile with a normal drill bit. It will crack.
I tried to use a diamond bit, but a diamond bit is shaped like a hollow cylinder on the end--there's no point. If you're drilling into slick tile, it's really tough to get it to catch and start grinding away at the tile. In fact, I never really got it. I think it would be easier if you were drilling into tile on the ground, but there's no easy way to stabilize it on the wall. I think you could create a template out of a piece of wood, but that's still an extra step.
Once the anchors are in, you can put your bracket back up and tighten your screws. Be sure to not over tighten them--it will crack the tile. Don't ask me how I know.