I drain down as far as possible using siphon method, then use shop vac to get out remaining water. Do it on a calm sunny day, so you get some air drying time also.
Following all this, the pool is still guaranteed not to be completely dry, since the top diameter is smaller than the base diameter, so you have that area all around the pool where the collapsed ring and pool wall are sheltering more wet spots and small puddles. I use a pile of swim towels to dry all this remaining water (crouching inside the empty pool, and burrowing under the collapsed wall to get at all the areas needing attention). This part is lots of fun (not).
Once you have the air ring completely empty, and sort of zig-zag folded (in other words, the pool is now a flat circle on the ground, with the walls and ring folded inward as neatly as you can manage), you start folding up the pool on itself, exposing the underside. Here is another cleaning and drying step; often there is various organic stuff that has been flourishing under there during the summer, as well as wet dirt or sand (setting up the pool on a tarp doesn't prevent the mess, although I'm sure it would be a lot worse without the tarp). I usually let the exposed portions of pool bottom dry in the sun for a while after cleaning, before going on to the next lengthwise folding step.
I would definitely advise a larger container than the original box (we use one of those car rooftop carriers -- like a giant fast food box -- works well for an 18' ring top pool), as trying to get the pool back down to the original package size sounds extremely frustrating. The whole job is tedious enough without adding that challenge, IMO! Also, the original box would not be mouse resistant, which definitely matters where we live.
Our pool is always put away clean and dry, and has been pleasant to work with the next spring as a result. We did have two cracks in the ring this year (at fold points) -- I will try the baby powder approach recommended by the previous poster, to see if it helps this year. However, maybe the ring is just getting more brittle after several seasons of sun exposure.
Usually I do all of the cleaning, drying, putting away myself -- so it definitely can be a one-person job. It's not fast work, though, so be patient and do other outdoor fall chores while waiting for the next step on the pool.
P.S. The swim towels that are used for cleaning and drying the pool (usually about half a dozen of them) require a run through the laundry with bleach after this process.
Once all the water is removed, it's probably best to let the vinyl air-out for a while to get it as dry as possible before you fold it up and store it to avoid algae growth. If you have the original box, it may be a good idea to try and store it in there as best as you can for protection from punctures and such during storage. The pump, filter, and equipment should be drained and moved somewhere out of the winter elements if possible. Perhaps a shed or spot in the garage if you have it. Perhaps others will have a thought or two. Have a nice evening.
