Welcome Sazzle!
To start, I would cut down and remove as much vegetation as you can from around and inside the base of that structure.
After that, with your vision unobstructed, make an assessment of the strength of the structure. Is it solid, not wobbly, no insect damage? Anything that you think would make completing it not worth the time or investment. Also, make an assessment of what you want to do with it if you decide to complete it. Will it be just a tool/storage/potting shed? Will it need power of some sort (e.g., lighting, etc.)? Or do you have more involved plans for it?
If you are not a do-it-yourself type, that inspection step, and the next steps, might require hiring a handyman. I'm not sure if a shed would need to conform to any type of building code, but you might want to ask. At a minimum, you would want roofing panels and some sort of cladding for the sides. For roofing and cladding, consider clear corrugated PVC or fiberglass materials that will let in a little light so that you can work.
If proceeding forward sounds like too much of an expense, or too much trouble, I thought of a use for it in it's current condition. Could it serve as a sort of whimsical grape arbor, or an arbor for Wisteria or other blooming vines?
