Interesting. I’m going to use the word “acquire” to denote a card becoming your card (i.e. it is included in your deck at end of game, unless at some point it is “unacquired”).
Ways to acquire a card:
* Anytime you gain a card, in any way and for any reason.
* A card is passed or put into your hand (assuming it wasn’t already yours). Precedent: Masquerade, Fortress
* Anytime you Exile a card (assuming it wasn’t already yours).
* Anytime you set aside a card (assuming it wasn’t already your card). Precedent: Inheritance …
* (unless the original instruction later moves the card somewhere else you don’t control(?), e.g. the Supply) Precedent: none?
* Anytime you play a card (assuming it wasn’t already yours). Precedent: Trail
—hypotheticals—
* A card is put or passed into a zone you control, e.g. deck, play area, Tavern mat (assuming it wasn’t already yours). Precedent: none, other than the scenarios already covered
That was fun. Did I miss any? I thought I could come up with more hypotheticals, but alas I am tired this week.
And I’ll leave it someone else for the unacquire list. 
I wish I had thought to use “acquire” instead of “get” when I wrote this thread 7 years ago: http://forum.dominionstrategy.com/index.php?topic=13116.0
I think Trail / playing a card is the only thing to add to my list since last time I edited it.
You missed Exchange. And actually we both missed buying a card. A card you buy becomes yours before you gain it, although with the new errata removing all on-buy triggers, I don’t think this distinction would ever matter.
That thread was a funny read! Ack I missed
exchange, dang; I might make some edits later.
I wasn’t including cases where a card was technically
unacquired, but naturally becomes yours again by the time all effects have resolved (Possession).
The
buy thing is interesting, since by definition you
gain the card anyway unless instructed otherwise. Does that mean a Possessed player technically owned a bought card before the Possessor did? Also, have there been any cases where 1. You buy a card. 2. It is interrupted by some trigger, and never subsequently
gained. 3. It is still
acquired by end of the turn. 4. And none of the other methods we listed above occurred (which would cause it to be
acquired regardless)? If not, then I’m not as concerned
Your point regarding Play also isn't fully accurate. You should say "unless instructed to leave it somewhere". And actually, entering a zone you control covers everything.
I see what you mean with your first sentence. But, I mean, you can choose to add a sentence similar to that as an addendum to any process, or you can leave it out, assume it’s implied, and save yourself some time. (says the guy who put the same assumption on almost every line)

But I might edit it in, thank you.
For your second sentence, sure, that’s another definition of what we’re talking about. But just stating it is a bit circular; that doesn’t give us the fun list.
