I'm often wrong, but it was my understanding that only rated games against the computer can be saved. Must be some basic chess apps out there that will let you do that though; chess.com's specialty is online chess against other humans (well, mostly humans...LOL).
How Do I Save A Game?

Well, that's a bit of a drag... I'd like to concentrate my activities on this site, but I'm such a noob that I want to learn a few ropes before I engage other actual humans.
What do you mean by "rated games against the computer"? How do I access/enable that?
--P

Haven't a clue how to access it on an iPad, but there are two ways to play the computer. On a PC, you can choose Play and then have a few options. Play Computer is the unrated version, but Play Live also has a computer opponent (only it's rated) as one of your optional opponents. That option had disappeared for awhile since someone had figured out a way to game the system by playing level 1 over and over again. It's back though, and with a new engine. Hope that helps. I'd go over there and try and find more for you, but I usually end up accidentally starting a game...LOL.
I posted this question to the site/app support team, but two days later no response. I suspect I'll do better here:
Suppose I start a game (against the computer) on the app on my iPad. But I can't finish the game in the first sitting. How do I save the game so that I can return to it next time I open the app, or, if I want to later open the app on my iPhone?
Seems like it should be an easy thing to do but.... no.
Thanks,
--PS