Theorycraft & Proxies
Two ways to put a card in a deck without pulling a real copy out of your collection. Theorycraft is for planning a deck you don't own yet. A proxy is a stand-in for a card you do own, so one real copy can back more than one deck, or stay safe in a binder while the deck plays a stand-in.
They never mix. Theorycraft decks don't use proxies, because a card there is owned or it isn't.
Underneath both is the rule the whole collection runs on: a copy you own is either a spare or in exactly one deck. Neither of these bends it. The deck modes are in The Three Modes.
Theorycraft: Planning a Deck
Theorycraft is "I'm planning a deck I don't fully own yet." Every card starts as not owned. It's for pricing out a deck before you buy, working from a list you copied off EDHREC or a friend, or turning a brew into a shopping list.
Pick it at the first step of New Deck / Import, or switch a deck to it from its settings. Start empty, from a precon, or from an imported list, and the whole list comes in as not owned. When you add cards, the search lets you pick between All cards and Owned, because a deck you're building toward is usually a mix of both. The line under the search box says Planning only, since adding a card here never touches your collection.
Keeping Count
The header keeps count of what you've got: 64 of 100. On each card there are two ways to say you've got it, and they mean different things:
Use from collection shows up when you have a spare. It puts that copy in this deck. Nothing new is added, because it's a card you already had.
I got it is for a card you just bought. It adds a new copy to your collection, in this deck.
A playset can be owned one copy at a time (I got one). If a bunch of the deck is already sitting in your collection, the Use N spares button at the top of the deck does them all in one go.
Changing your mind is safe. Not owned after all leaves the copy in your collection as a spare rather than deleting it. Saying the deck doesn't have it is a statement about the deck, not permission to destroy a card you may well own.
The Shopping List
Under the Export button, Need is everything you haven't got yet and Have is every copy you own in the deck. Each comes as plain text (1 Sol Ring), TCGplayer (it pastes straight into their Mass Entry box, with set and collector number), or CSV. The deck's value and its Stats page work the same as on any other deck, so you can see what the whole thing would cost before you spend anything.
Suggestions in the deck builder give a Theorycraft deck three cards you own and one to consider getting.
Finishing It
Once you own it all, switch it to Builder or Catalog from its settings. Leaving Theorycraft needs every card to be owned, because those decks only hold cards you own. If some aren't, it asks: Keep as Theorycraft and keep collecting, or Mark all owned now, which uses your spares first and adds the rest as new copies.
Proxies: The Rule
A proxy stands in for a card, not a particular printing. The rule is simple: you can proxy a card if you own at least one real copy of it, in any printing. The proxy can look like whichever printing you want, the fancy one included, and it never uses up your real copy. That's on purpose. If your real one lives in a slab in a display case, it stays a spare, and the deck plays a proxy of it.
That's also why you can't proxy a card you've never owned. A deck full of stand-ins for cards you don't have is a plan, and that's what Theorycraft is for.
Where Proxies Come From
Builder decks make them for you. A card uses a spare of that exact printing. If you don't have a spare of that printing but you own the card in another one, it goes in as a proxy, your real copy stays a spare, and the message after you add it says so.
Proxy, next to Add when you hover a search result in the deck builder, adds one on purpose.
Mark as proxy in a card's details turns a real copy into a proxy. The real copy stays in your collection, now as a spare.
Deck builder suggestions offer a card As proxy when every copy you own is already in another deck, and Pro Analysis has a whole Proxies group for the same thing. See Pro Analysis & Combos.
Quick Swap brings a card in as a proxy when all your copies are in other decks.
Swap printing on a Builder deck uses a spare of the new printing if you have one, and otherwise keeps it as a proxy, with your original copy going back to being a spare.
Scanning: a scanned card is a real card, so it only comes in as a proxy if you mark it Proxy in the queue before you approve it, and only for a card you own a real copy of.
Making a Proxy Real
Got the real card? Open the proxy's details and press the orange Proxy button to turn it back into a real copy.
On a Builder deck it uses a spare of that printing. If there isn't one, it asks Do you have this card? That's for a real card that never made it into your collection (a precon you never logged, say): I have it, add it adds the copy to your collection, in this deck. Close the question and nothing changes.
On a Catalog deck the card is in your hand, so making it real adds it to your collection as a new copy.
Either way it tells you how many you have now.
How Proxies Count
Your collection doesn't count proxies at all. They aren't copies, so they don't change your totals, your unique count, or what your collection is worth.
The deck shows them with an orange badge, and its status reads Includes Proxies. A deck with proxies doesn't count as built from cards you own until they're real.
Value is split: the deck's header and its Stats page show Real and Proxies separately, so you can see what the deck actually cost you against what it would cost to own outright.
Export has a Proxied list on Builder and Catalog decks, for when you'd rather buy the real thing.
Combos and synergies know where your copies are, so a missing piece reads "yours is in" another deck, by name, rather than "not owned."
Removing a proxy just takes it out. There's no "do you still have it?" question, because there's no copy behind it.
When a Proxy Goes Wrong
If a deck has a proxy of a card you don't own in any printing anymore (say you sold your last one), the deck shows as Illegal and names the card, with what to do about it: remove the proxy, or switch the deck to Theorycraft. Going to Theorycraft turns every proxy into "not owned," since Theorycraft doesn't have proxies, and the cards you do own stay right where they are.