You need a flat bladed razor (they're sold as paint scrapers, I think), a pack of blades, and a tube of silicone. Scrape all the old silicone off the seams. It will take a long time. Then clean the seams with rubbing alcohol.
Tape off the size of the bead you want to add (painter's tape works well) and apply the silicone. Use a plastic spoon to smooth it out. Work quickly, because it starts to solidify fast and it will look awful if you try and work with it for too long.
GE silicone I window and door is what I use, it is easy to find and works well. 2 tubes should will be enough, 1 probably won't, unless you don't apply it very thick.
It stinks for a day or two, and it makes your eyes burn a bit if you stick your head in the tank while applying it.