This could be a little tricky as there is a risk of damaging the tile; it can be done of course but if you are not used to taking on this type of projects yourself, perhaps look for a pro to assist you.

Having said that, there are several DIY videos on you tube, but my first question would be, what type of tile do you have (ceramic, porcelain)?

You should find the wall studs and hang using them for support. A high speed drill with a small concrete drill bit and then use a larger drill bit to fit the size screws you use to hang your mirror from.

These between the grout lines. No studs, no worries.

Right Joe, those cheap things are good for a wash cloth.

I've hung 20 lb weight from one of these for several hours without any damage to the wall and without anything falling. They work great.