If your hand slips while you're dusting, and your favorite glass vase falls to the floor and breaks, you may be able to repair the vase well enough to once again hold water, but it's never going to be the same. Short of reheating the glass to fuse it, virtually no process will eliminate the hairline cracks left over after gluing the pieces back together, even if you minimize the cracks by carefully aligning the pieces. You need waterproof glue, and although it takes more time to harden than cyanoacrylate, two-part epoxy resin is the best adhesive for the job.
Collect all the pieces of the broken vase. The repair probably isn't worth doing if the vase has broken into several small pieces, or some pieces are chipped. The repair is most likely to be successful if the vase has broken into two or three large pieces, or if one small section, such as the lip around the opening, broke off.
Clean dirt off the pieces you are going to glue with a rag and dry them thoroughly with a clean cloth. Pay special attention to the edges that you're going to glue together.
Support the vase in a holder if it doesn't stand by itself. Test-fit the pieces you are going to glue so that you know the best way to put them together to minimize visible crack lines.
Mix clear two-part epoxy glue with the hardener that comes with it on a piece of scrap cardboard. To get the strongest repair, use a product that takes longer than 5 minutes to set -- it will be less brittle than one that sets quickly. Mix only what you need for the repair -- you'll have to discard what you don't use.
Spread the epoxy on the edges of one of the pieces of glass you need to glue, using a toothpick. You don't need to apply the glue to both surfaces of a joint, as long as you spread it evenly. Try not to leave voids, but don't use too much glue, or you may have trouble cleaning the glass after the glue sets.
Fit the pieces together and keep holding while you dab hot-melt glue on one or two places along the joint to keep the pieces together. You can scrape off the glue after the epoxy sets.
Wait for the epoxy to stiffen; before it hardens, scrape off any that has oozed out the cracks, using a razor blade. After the recommended setting time for the glue you're using has elapsed, scrape off the hot-melt glue with the razor blade.