Here's a good written set of directions, but check the YouTube videos as well...
Fixing a Leaking Aquarium
If it were me, I would go ahead and reseal the whole tank because the new silicone wont stick to old silicone very well.
One word of caution: Be POSITIVE that the silicone is safe for your tank. Use a clear 100% silicone like GE Type I,
http://www.lowes.com/pd_35166-72643-LW012X4_0__?productId=3078887&Ntt=type+i+silicone& pl=1¤tURL=%2Fpl__0__s%3FNtt%3Dtype%2Bi%2Bsil icone%26page%3D2&facetInfo NOT Type II
. Do NOT use any with coloring, mildew inhibitors or anything else. (They also sell this in single tubes. My 55 gallon used 2 tubes)
Be prepared to take your time and do it right, but on the other hand you need to work quickly when you apply the silicone because the silicone starts setting in about 10 - 15 minutes depending on temperature, humidity and air flow. A second pair of hands would be a great asset.
Use a razor blade and remove the old sealant. Clean the glass with ammonia, removing all smudges or fingerprints from the glass.
Tape off the glass using masking tape or painters tape all the way around with the tape about 3/8" from the edges, adding short lengths off at an angle as a 'pull tab'. When applying the silicone, work in short lengths (about 2 feet) at a time. Apply the silicone and use something rounded like a tongue depressor to force the silicone fully into the edge and to taper the silicone.
Silicone STINKS like vinegar. Keep your work area well ventilated. If your tank is so large you have to stick your head in to work, it is a little hard to breathe. If you have a garage to do the task, I would do it there.
Pull off the tape as you finish the side, before the silicone starts to 'skim over' or you will have a mess. Leave any drops or smears on the glass. You can clean that up with a razor blade after it cures.
When you are done, let the tank set for a minimum of 24 hours. More time is better (I let mine sit for 3 days, but I tend to err on the cautious side).
After the silicone cures, take the tank to the garage or any other place where you can sit it level before filling the tank (anywhere but inside the house. I say to take it outside in case it is still leaking ). Fill it up and let the tank sit for 3 days to make sure the seals hold. If the tank leaks, you have to start all over.
If you did a good job and the tank is sealed, drain it out and use your razor to clean up any drops or smears on the glass that shouldnt be there. Take the tank in and set it up.