Whether you broke your favourite glass sculpture or you simply want to experiment with glassmaking and repair, you can consider yourself lucky. Glass is a relatively easy material to work with and can be fun to manipulate, as well. One positive feature of glass is that once it reaches reach its melting point, it continues to maintain its structural integrity. At the same time, however, you can bend, manipulate and even adhere the glass to other glass pieces.
Put on a pair of protective goggles and a pair of thick, fireproof gloves. Since glass gets hot, you'll want to protect both your hands and your face from getting burnt. To be even more cautious, consider wearing a long sleeve shirt.
Turn on your blowtorch or Bunsen burner and adjust the flame so that it's blue. Either works fine, but if you want to keep both hands free, a Bunsen burner is the better choice.
Hold the broken edge of the glass pipe above the flame, then carefully lower the glass so that it's inside the flame. Hold it there until you notice the glass begin to melt or bend. If necessary, heat the other piece of broken glass to smooth out any broken edges.
Adhere the broken piece of glass pipe to the other piece. Hold it in place until the glass cools down and the two pieces stick together without being held. Set the glass pipe aside on a piece of newspaper or foil and wait until it cools completely.