I've done a few tanks, and here are the directions I've used with success: DIY Tank Re-Seal Full Instructions - Aquarium Advice - Aquarium Forum Community
I've used both Aquarium Sealant you buy specifically for aquariums, and 100% Silicone from a hardware store. As long as it says "100% Silicone", you're golden. I, personally, hated the aquarium specific stuff. It was hard for me to squeeze, I could not get an even bead, and I could not get a thick enough bead. It leaked and I ended up having to completely re-seal it. I much preferred the stuff that goes in a caulk gun. Cut the tip so you have about a 45 degree bevel. Cut your tip small at first, test your bead size, and cut larger if need be. But be aware that I've heard the caulk guns can be cumbersome on smaller tanks.
So, just to hit a few points, some of which that have been covered but are important:
The safest way is to remove all the old interior silicone, as the new silicone will not bond with the old silicone.
Look at a tank that has a relatively new and original seal so that you'll have a feel for how much silicone to use.
Remember to stop your bead about 1" or so from the end, because when you smooth the bead your finger will drag some silicone to the end.
I wore a latex glove when smoothing the bead. After you dip your finger in the alcohol, really put a good bit of pressure into smoothing the bead. you really want to squish it into the corners and get out bubbles.
I would seal the bottom pane first, then do the sides from the bottom up. This will give you a neater look. When you're doing the side seams, do the one on your left first (if you're right handed) so that you don't accidentally smear the fresh seam with your arm.
Let it cure for 72 hours. Be sure to leak test it for at least 3 days. And don't forget to do a victory lap for a job well done!