If your old tank is a leaker, be careful following the instructions that the Biffster has linked to. It is fine for resealing a tank that is structurally sound, but a tank that has a significant leak probably has started to separate a piece of glass from the other pieces. That kind of situation is not just a leak but is a break down of the actual structural strength of the tank. The only good way to reseal a tank that has seams starting to fail is by rebuilding the tank. There are lots of similar blog posts on how to build a tank from scratch that would be far more pertinent in that situation. Removing all of the old silicone and the plastic frame could be done in much the same manner as that strip showed but the goal would be to strip all the way down to nothing but raw pieces of glass and build a new tank with some old parts, like the glass and the plastic frame. The closest I have come to doing that was to replace a broken front glass on one of my old tanks. I got the tank for almost nothing since the front glass was cracked all the way across. A new piece of glass and plenty of gutsy assembly by a total tyro gave me a tank that has served me well for about 30 years now. I presently have a 60 gallon tank that started to come apart in place and has been replaced. When I find the time, I will be constructing a new tank from that old one. I finally found a tool that will let me remove the old plastic top frame from the glass ends and sides so that is one obstacle that I have overcome. It means that the new tank can use the same frame as the one that came off it in the first place.
The tool I found is not designed for aquariums at all but is intended to use for finishing grout joints in concrete work. The fact that I can use it to separate the plastic trim from the glass is something I determined while I was in the DIY shop thinking about the tool design that I needed and when I got it home it seemed to work fine for that.