Drilling and cutting glass tiles

You need a set of these:

For a straight cut, score the tile with a glass cutter and break it over a pencil. Or if the tiles are too small for that, or you are only cutting a small piece off, score with the glass cutter and nibble off the waste with pincers. It would be worth doing it a few times for practice beforehand. There may be quite a few wasted tiles.

I have also cut glass with a cutting disc in a Dremel. I don't know if you are supposed to do that. ;-)

Try searching on Google or even YouTube for "drilling glass" and "cutting glass".

Ideally, by drilling it vertically on a drill press, rather than when it's on the wall. Glass drills easily, the problem is vibration and unpredictable forces causing it to crack as well. A stable drill press solves much of this.

You can drill small holes in glass using a glass drill bit, a leaf- shaped carbide spear. Many people also use these for starting through the surface of hard tiles. Quality of them varies a lot, mine have all been hand-honed with a diamond stone to ensure their centre chisel point is accurately on-axis (the cheapies aren't, but can be fixed). You can also drill glass using a copper tube core drill and abrasive, but that's only for big holes.

When drilling, you need a lubricant. Make a circular dam of vaseline and fill it with white spirit, turps, paraffin or diesel. Vaseline, unlike blu-tack or putty, remains attached to the glass when oily. For repeated work on small pieces, setting up a "bathtub" of paraffin with a shallow tin is quicker (but use a backer board inside, so that you don't drill through the tin!).

Drill with a gentle "dabbing" motion to keep the glass swarf clear. It doesn't self-clear as metal or wood chips do.

For sawing, a wet tile saw works fairly well, but expect a higher failure rate. You might find a fresh diamond blade, kept only for working glass, is useful.

or these.