A big thanks to fishfurfeather.com for this article.
Article originally from http://www.fishfurfeather.com/articles.php?article=repairing_a_leaking_aquarium
This article is designed to guide you through the steps involved in repairing a leaking aquarium, either by repairing a leaking seam or replacing a broken panel.
As almost all aquariums are now all glass without frames this article will only refer to repairs to these aquariums.
The first step is to identify the exact place of the leak. If it is a split panel than it is obvious but if the seam is leaking it is important to be sure of the exact point of the leak as the water can run round the edge of the aquarium before dripping onto the floor.
Once the leak is identified then the aquarium should be drained and all rocks and gravel removed. The fish and plants should be placed in any suitable container with the heater and filter, covered and left alone (they will be perfectly OK for a couple of days). Once the aquarium is dry the old silicone must be removed. If a panel is being replaced then all the silicone from around the panel must be removed, if a leaking seam is being replaced then all the silicone from the entire seam must be removed. A silicone remover available from most DIY shops will soften the silicone and allow its easy removal. Once the bulk of the silicone is removed the rest can be removed with a sharp knife or a razor blade. If a panel is being removed then be careful as glass is sharp, but with care the panel can be removed without breaking. Next step is to measure the exact size and thickness of the glass required before ordering from your local glazier, remember to get the edges ground as cut glass is very sharp.
Once the area to be repaired is clean of all silicone then the area must be cleaned with meths or alcohol, to remove any grease (note do not clean the area with anything that may leave a residue and stop the silicone sticking). Next secure the new pane of glass in place with sticky tape on the outside.
You are now ready to silicone (you must use an aquarium silicone as this does not contain any fungicides), cut the nozzle at 45 degrees, and pull the silicone bead in a smooth and steady motion so you have a continuous line of silicone between the two pieces of glass. Now using a wet finger go over the wet silicone in one motion so that the bead is pushed into the joint and continue so it over laps the existing silicone.
Finally leave the silicone 48 hours to dry before filling with water and testing, leave full for at least a couple of hours to ensure that it is not leaking and to make sure any chemical residue is removed from the silicone. As long as all is well the aquarium can now be drained and re-filled, a de-chlorinator added and once it is up to temperature the heater and filter can be added and then the fish.
With any luck you now have non leaking aquarium.