To make a hole in seaglass i personally use a drill press but this is a big power tool and one that i suggest you do not use. What i recommend you do try is a tool called the Dremel which is inexpensive and will fit in your hand. You can buy these at any home improvement stores such as Home Depot or Loews. The next thing you must purchase are Diamond tipped drill bits which you can find on the internet or ebay. You can also use carbide glass & tile bits but these wear out extremely fast and are much more likely to cause you to break or chip the seaglass and are better left to people with more experience. The .084 to 1mm ball tipped Diamond drill bit should meet all your needs right now.  

The third and last item is a bowl, dish or pan that you will fill with water till it submerges the entire piece of seaglass. the water acts as a lubricant for the drill bit and also keeps it cool so the heat caused by the bit's friction does not crack the glass! OK, let's get started.........

The first thing i do is take a magic marker and place a dot on the front and back of the seaglass exactly where i want my hole(s) to be. I then place the seaglass in the pan making sure that it's completely covered with water. You are now ready to turn on your Dremel or Drill press. Place the bit over the mark you made on the front of the glass and start your hole being sure you occasionally back out the bit to remove any glass sludge from forming. (Tip) Drill halfway through the seaglass from the front and then turn the glass over and finish drilling from the back, this will eliminate chipping and assure you of a nice clean hole. That's it!!! Be sure to take your time and don't rush and i strongly recommend practicing on some damaged pieces of seaglass and in no time you'll be drilling holes just like a pro!