If you have a good solid deck, you have a great start to a screened porch. All you need are some posts, some headers across the top and some roofing, if your deck is open. Of course, you'll also need screens on the sides and probably a door. You also will need to check local building codes for any requirements or restrictions and for any permits. You need to take good measurements, to buy framing materials and to decide whether you use ready-made screens or install screening yourself.
Measure and plan. Take precise measurements of your deck--and hope the dimensions will fit standard materials. Then plan your porch: decide where you want doors, whether you want screening the full height or just part way, whether you want permanent screening or screened sections you can remove. Decide how you will set framing posts, what size you will need and how many. Choose a roof (unless your deck is already covered)--flat, slanted or pitched. Then calculate the materials you will need--lumber, screens, roofing--and figure the cost.
Set your framing posts. At a minimum, this will be one at each corner of the deck but a big porch may need more. It will be easiest to fasten metal post holders on the deck and then mount your posts (4 by 4 or 6 by 6) in them. These attach with big screws; use big lag screws to attach posts to the existing house wall. Then nail a 2 by 4 (or 2 by 6) header on top of them. Depending on the height and length of the side and how you will be installing screening, you may want to add a bottom (sill) plate and another 2 by 4 part way up. You may want to cut notches in your posts for the headers for extra support. You also may elect to add diagonal bracing at the corners.
Install your rafters or roof framing. You can use purchased rafters for a pitched roof to be covered with shingles, you can place roof joists from your side walls for a flat roof or you can use framing lumber to build supports for a lightweight fiberglass or similar roofing material. If you are building a flat roof, allow some slant to drain water. Unless you use fiberglass or transluscent plastic, the roof should be decked with plywood or similar material, then covered with roofing paper and shingles.
Add doors and other elements. You'll have to build a frame for a door (you can buy a screened door or make one yourself) and add any shelves or siding partway up the walls. Many screened porches are build with siding about halfway up, then screening on to the roof. This is a matter of personal preference.
Screen it in. You can use purchased screen panels and fit them in with framing, attaching them with screws or other fasteners. That would make them removable. But for a true screened porch, install your own screening, using either traditional metal or more weather-resistant vinyl. You can buy screening systems that use a base in which a rubber spline is rolled to hold the screening. Install the base tracks, then fasten the top by rolling rubber spline into the groove. Then work your way down the sides, pulling the screening taut as you go. Do the bottom last and pull the screening as tight as you can. The spline will help tighten the screening. You may wish to cover the splined area with wood or vinyl caps.