Empty the aquarium of all fish, plants, water gravel, pumps and filters and dry the inside of the aquarium.
Cut away the old silicone sealant bead from the inside of the aquarium in the corners of the tank that have the broken glass. For example, if the broken pane is the front glass. Remove the silicone seal from the front left corner, front right corner and front bottom edge. A flat razor blade does an excellent job of getting under the silicone and peeling the material away. Have a second person hold the glass pane as you cut the silicone away to prevent it from falling and shattering.
Take the glass pane to a glass shop and have them cut you a piece of replacement glass.
Prep the glass surfaces for the silicone. Make sure every bit of the old silicone is scraped off the remaining panes of glass where you will place new silicone. Clean all the mating surfaces with a degreaser like naphtha. After cleaning the mating edges of the glass, do not touch them with your hands again. Any oils from your hands could cause the seal to fail.
Place the glass back into the aquarium. The plastic rim on the top of the tank and on the bottom of the tank will help you line up the glass. Have a second person hold the glass against the plastic rims while you install the sealer.
Place a bead of sealer in the front left corner, front right corner and bottom edge of the glass inside the tank. Make the bead thick just like the existing bead in the tank. Go slow and make sure there are no gaps.
Allow the tank 24 hours to fully dry. Fill the tank one-quarter of the way every two hours. Allow the tank to sit for a week before placing fish back in. This allows the silicone to "outgas" and gives the tank long enough to break. If it does break, it is better not to have fish in the tank.