Always wear safety glasses! (It's a good idea with any drilling, but especially when drilling through glass.)
There are specialty bits made for drilling through glass that can be found at most hardware stores. A standard drill will work fine. Don't use a hammer drill! Keep your drill speed low (if it is variable) especially if you wind up using a diamond bit.
Lubricate the hole. Otherwise, you will probably crack your work piece through thermal stress. There are specialty oils sold as a glass drilling lubricant, but WD-40 works just fine and is easy to apply (with the included straw applicator). I've never used water, but I'm told it can work, too. Whatever lubricant you use, make sure you don't get it on your drill. Don't overapply it, but replace what runs off/evaporates.
Putting a piece of tape over your starting point can help keep your bit from sliding out of place.
When you are done, let the piece thoroughly cool before cleaning it or it can crack. Even if it feels cool to the touch, it might still be enough of a rapid temperature change to cause a crack. (Cleaning will remove small bits of glass and whatever lubricant you used - so it's a good idea.)