It would be easier if you just tried it out.
It's a standalone Java executable so you do need Java installed, but you probably already have it because many applications are written in Java. It has nothing to do directly with the game, so you do not need a special shortcut because of GoMule.
When you run the program you get a more or less empty window in front of you, simialr to a regular windows file explorer. You can open existing characters and open or create "stashes", this is where you can store your items. Opening a character will need access to the save, specifically the d2s file.
Once you open a character you can see all the items with their graphic, hovering over each will reveal it's stats and the fingerprint, which was previously mentioned. Clicking on any item will transfer it into temporary space, clicking on an empty space in your character's inverntory, cube or stash will put the last item you took there. You can also create an external stash which can hold thousands of items. It will slow down if you cram too much stuff into it, but you can just make another one.
These are the basics, you can do much more regarding stash management with GoMule.
Edit: thanks Vildecor for dropping a screnshot, I'm away from my gaming PC so I couldn't