How do I enclose my desk?

You will need a CO from your town first...that doesn't look like it is condusive to that project.

https://www.doityourself.com/stry/encloseaporch

Honestly, this deck does not appear to have the structure to support this. Please consult a licensed contractor who will get a building permit for this job.

Totally agree that you need to make sure it is structurally able to add on those changes.

Definitely undersupported, even as it is now. It may not pass an inspection now.

I certainly agree with the concerns about the stability of the structure, and wonder if you referring to the top or the bottom part? If you want to enclose the bottom, just use screening. Instead of building a floor, have you thought of using paving stones or even sidewalk blocks? As for the top, If you want shade why not attach an awning to the house and go with that. I urge you to really consider the stability/safety of the initial structure.

Contact a local contractor as suggested above

I'm sorry to tell you, but I don't think you'll be able to enclose your deck without major work. I don't know if it even has footings? The posts used to hold up your deck are not rated to hold the extra weight that you'll be adding. And it is a lot. You've got studs, drywall, plywood for the exterior, roof and floor, siding on the plywood, flooring, roofing materials, furniture when completed, and the list keeps going. You really need to get a licensed and insured contractor out there to see what can and can't be done.

Are you trying to stop water, wind and dust etc from entering the top or bottom section?

If it's the bottom a small self enclosed room may be the answer. If it's the top then a bit more planning is needed.

What is the building code? Check with your local government office.