I did this to a 65 gallon Craigslist tank last year and learned a lot. I completely removed the bottom panel, stripped out all the sealing silicone, cleaned all the surfaces thoroughly, reseamed the bottom and resealed it and it's been fine.
First, you want to check the seams. That's the structural part of the tank. Those top and bottom trim pieces aren't that hard to remove by sliding a metal putty knife between the glass and the trim and then carefully pushing them off. That will give you the ability to check the panel-to-panel adhesion. Any edge where a panel butts against another, look through the glass and you should be able to see if there are any gaps in the silicon adhesive. Just my opinion, but if you see any gaps bigger than an inch long, or if over the length of the edge you see anything less than about 98% adhesion, you should break it all the way down.
It could be you only need to reseal it in which case you'll need to scrape all the old stuff off and thoroughly strip any remnants of the old silicone off the glass. That's the trickiest, most tedious, but most important part. Silicone won't give up easily and you'll need a very sharp scraper and some acetone. I was having trouble with the acetone since it doesn't readily dissolve the old silicone. What I found, oddly enough, was that purple PVC plumbing prep worked pretty well. It won't dissolve the silicone but letting it set for a minute will seem to harden it and make it easier to scrape off. I since heard it's mostly acetone, but whatever. Even then you'll want to go at it lightly with some fine steel wool. You need to remove it all as new silicone won't stick to old.
Then it's a matter of reseaming (if needed) and resealing it. I went with the Aqueon product which is a little pricier than the Big Box (DAP, or GE) sealants many go with, but this being my first time I wasn't cutting any corners. Fishman on YT has some great video of a custom tank he built a couple years ago which showed me how careful you need to be. He's about as meticulous as they come.