If you have stuck a band-aid over the wound with the glass piece under the skin, the first thing you need to do is to remove the band-aid. Keeping a band-aid for a long period will allow infection to set in. The methods to remove the glass piece from under the skin will depend on the size of the piece and how deep it has embedded under the skin.
To begin with wash the area clean with soap, gently. If the piece is not large, you may use duct tape or scotch tape to remove it. Place the tape firmly over the area where the glass piece is embedded and let the tape remain on your skin for some time. Then press over the area gently to ensure that the glass piece gets stuck to the tape. Now pull the tape off slowly and gently. You can repeat the process twice or thrice to remove all the pieces (if there are more than one). Even when you remove the band-aid, it may help to remove the glass shards. You can also make use of hair removing wax cloths or body wax to remove the pieces.
The best thing would be to soak the area in warm water or water mixed with hydrogen peroxide or Epsom salt to allow the piece to come up and then you may remove it by using scotch or duct tape. If the piece is way deep under the skin soak, you can try to remove it with a pair of tweezers. You can also try to insert a needle gently in the area and remove it. You can use a magnifying glass to locate the glass piece. Do ensure that you’ve disinfected any needle or tweezers that you use.
You can also squeeze out the shard of glass, similar to how you pop a pimple. It could be painful but it usually works. You can apply some alcohol on the area to prevent infection. One of the oldest remedies is to put a piece of bacon on the splinter, wrap it over the area, leave it overnight, and remove it in the morning. You will find the glass splinter gone.
You can use glue to remove glass piece. Apply some glue on the area and leave it for a while. Once it is dry pull off the glue sharply to remove the glass piece.
If you find the glass pieces still beneath the skin and you have tried all these methods to remove it, it is best if you go to the doctor instead of risking infection. If the glass piece has become wedged horizontally, it is a good idea to consult the doctor right away, as it may involve cutting the skin to remove it.