Tags
Tags are your own labels for cards: "Commander staples", "Box 3", "Trade bait", anything. A card can have as many as you like.
Two kinds of tag
Card tags go on a card printing and cover every copy you own. You can tag a card you don't own yet, which makes tags handy for deck ideas.
Copy tags go on a specific group of your copies, such as your foil Near Mint ones, the way a binder held them. Different finishes and conditions can carry different tags.
A card has a tag if either kind has it. Searching or filtering by a tag finds both.
Adding tags
Open any card and use My tags. The top picker tags the card. Below it, each group of your copies has its own picker. Type to find a tag, or type a new name and press Enter to create it.
To tag many cards at once, use Select Multiple in your collection and the Add to... menu, or open Tag mode, pick a tag, and tap or drag cards onto it.
The Tags page
Tags in the sidebar lists every tag with how many cards carry it. From there you can rename, recolor, reorder or delete tags, and see each tag's cards. Renaming a tag to a name you already use offers to merge the two.
Searching with tags
tag:"Box 3" finds cards with your tag. Filter by your tags in the sidebar too, with Any or All.
otag:removal uses Scryfall's community tags for what a card does. function: and oracletag: work too.
art:squirrel uses Scryfall's community tags for what's in the art. atag: and arttag: work too.
Put - in front to leave a tag out: -tag:trade, -otag:board-wipe.
Typing tag:, otag: or art: suggests names as you go. These work in card search, your collection, and the deck builder.
Trade
Marking cards for trade is separate from tags. Use the trade toggle on a card, the bulk menus, or the For trade row in Tag mode. For-trade cards get an amber badge and appear on your public tradelist if you've made that section public.
Tags are private
Only you see your tags. They don't show on your public collection or decks.