I don't want to know how I can save a world online so I can play it anywhere, I want to know how to take a world you've been playing with online, and save it so you can play it later. Just had to clarify that, because Google seems to not know what I'm talking about.
If you're the server administrator you run a "save-all", either in console or as op in game and then you copy the world folder in question and download or move that to your %appdata%/.minecraft/saves folder. As it goes minecraft server does save automatically by default but it doesn't necessarily do it on the fly and thus the save-all command forces the save file to save correctly.
If you're not the server administrator then you can't, tho I have heard of tools that record visited chunks and generate a map off of that before, but that requires you manually visit literally every generated chunk and well, you're gunna have no idea what has already been generated and what you're generating by walking around.