How do I smooth, cut, and drill holes in glass found on the beach?
For drilling glass, drill bits for tiles (the spear-point type) work. Work wet and go slowly. I've seen them down to 3mm. You need to hold the glass steady, but a cordless drill will be adequate. 

If you want a smooth (as opposed to facetted) piece, jewellers rouge on a cloth will polish glass, worked by hand, though it might take a while. For a little reshaping, such as to remove a sharp edge, you can use wet/dry paper (silicon carbide paper) or emory cloth. Start coarse and work down to a fine grade before polishing. I'm much more familiar with machine polishing, but that's good for flat surfaces.

If you really need to cut it, small cuts can be made with a dremel or similar, with a carbide cutoff wheel. There are also coarse hand saws for tiles that cut glass. They're like a file made of thick wire (coated in abrasive) in a frame, rather than what you'd it think of as a saw.

Safety glasses are a good idea when cutting or drilling.