Is it possible to fuse sheets of the galvanized sheet metal that they sell at the hardware store for roofing together so that it is water tight?
I was thinking that this may be able to be accomplished with the same flux and solder used to fuse copper pipes, but I'm not sure.
The reason I am doing this is that I'm hoping to make some water tight trays that potted plants can be placed in.
You can make watertight trays from flat sheet metal without soldering or riviting.
Take a sheet of metal whose
Fold the sheet so it ends up looking like this:
You can fold up one side at a time using a piece of wood (maybe 1x2), a bit shorter than the length of the side you are working on, as a bending edge.
Work around the piece, clockwise or counterclockwise.
You will have to work the angle fold in the corners as you move to each successive side. The angle corners will point outward initially. Then you bend them inward toward the short end.
All edges will end up at the height of the sides with no seams. The easiest kind of waterproof.
Bread Tin Corner. How to make a water holding container without needing to solder it has been an age old necessity. You'll still see them used in cheaper bread pans, though hydroforming or stamping have taken over for the most part. 
Soldering galvanized sheeting is definitely possible, but with a lot of gotchas. Things like, you must use the right flux and the right solder and you must use a copper soldering iron, and if it's not the correct type of galvanizing, then it can't be soldered. So while soldering is the ideal method, it's a long shot. See: here
short of that, I personally would use STEEL rivets to build the box, and then use something like JB Weld to fill in the joints. The JB weld will provide both structural strength and waterproofing. Don't use aluminum rivets, as they'll corrode due to galvanic reaction.
Your question goes in a couple of different directions, but lets see:
Option #1 - Soldering galvanized steel
Soldering galvanized steel is very simple, yet, if compared to copper is a little trickier to get done. First, lets talk about the flux you should use.
My favorite method is a mixture 50/50 of 2 fluxes:
Muriatic acid: link at Amazon
Soldering fluid: link at Amazon
I actually prefer Johnson's (here), but I don't think you can buy it directly.
Directions:
1 - Mix 50% / 50% of both acids.
2 - Prepare the surface of the galvanized steel. This is not "necessary", but makes your life easier. Scrub the surface with a wire brush, or sand it down, scratch it, anything to make it less smooth to help the solder grip. Cheap Example:
Wire brush: Link at Amazon
3 - Have your soldering iron hot enough to melt solder (50/50 solder is fine).
4 - Solder like you would copper, except, make sure the flame is either turned of on your soldering iron, or that it doesn't make contact with the galvanized steel for too long. Basically, you have to be quick. If the flame burns the galvanized coating, it will turn black, and it'll make soldering extremely hard from that point on.
5 - You may want to grab an acid cup and brushes.
Option #2 - Welding galvanized steel
Welding galvanized steel is very possible. It is not as easy as welding plain steel, however, it is not that hard. One thing to note is that the smoke from welding galvanized steel is very toxic, and you should be prepared to take precautions to not get sick. You can then spray paint the area welded with some zinc pray for rust protection.
Option #3 - Boxing a panel
For metal roofing, specially standing seam (which I don't think its what you're referring to), many people simply don't do this step, and it is honestly not even recommended by some metal roof manufacturers, which is mind boggling to me. Some recommend to simply seal a joint or do other things with a z flashing for example and sealer. I'm only mentioning this because, the solution proposed by "bib" is the very best case scenario, since there is no cutting and soldering to waterproof. This should be always the go to method, whenever there is an opportunity to do so.
