For a small patio you build yourself, a simple concrete slab is probably the fastest, easiest, and least expensive. Just build a simple form with
2x4's and stakes, have concrete delivered (look for on site mixer for small jobs), screed, edge, done. You can go as fancy as you wish, coloring, stamping, staining, etc.Another option is concrete pavers. You can have them delivered, or haul a few home at a time. They look a bit nicer than a simple concrete slab, but cost a bit more and can be more labor intensive to install (preparing the base, tamping, screeding a sand layer, laying pavers, tamping, filling joints with sand, more tamping, etc). Of course, for a small area you could just grab a few 12" square pavers and lay them on the ground. They'll settle unevenly and will need to be reset over time, but it's a quick and dirty option.
You could also build a wooden deck. Ideally with concrete footings, joists, and decking. But you could also use Pressure Treated sleepers and attach the deck boards directly to those. You could even build small modules (2x2,
4x4, etc.) and lay them side by side.Another option is just to cover the area with gravel. It's not as attractive or usable as a patio, but it will keep the mud down. You'll probably track in small rocks and weeds will eventually grow in the gravel, but it's cheap and easy.
Anthony Watson