These are the standard published rules (Bicycle Cards' Rummy page, which follows Hoyle), rewritten in plain words. The rulebook wins any argument — this page just makes it easy to read.
Rummy is a matching game. You build melds — matched groups of cards — and try to be the first player with no cards left in your hand. A meld is either a set: three or four cards of the same rank (like three 8s), or a run: three or more cards in a row in the same suit (like the 5, 6, and 7 of hearts).
Players: 2–6. Rummy shines with more than two players; its famous two-player cousin Gin Rummy has its own page on this site. Ages: 8 and up.
What you need: one standard 52-card deck. Cards rank King high down to Ace low.
Where the Ace sits: Bicycle's rules rank the Ace low — a run can be Ace-2-3 but never Queen-King-Ace. Bicycle itself notes that in many forms of Rummy the Ace may rank either high or low. Gin Rummy also plays Ace low only. Decide before the deal if your table allows Ace-high runs; there is no single answer across the rule books.
Must I meld the moment I can? No — official. Melding and laying off are always a choice, on your turn only. Holding a meld back is legal, and it is how you set up going rummy.
Taking the upcard before the first turn: House rule in some books. Some published versions let the other players claim the first upcard before play begins. Bicycle's rules as printed start play with the player to the dealer's left drawing normally. Agree before you start.
Playing to a target score: House custom. Bicycle scores hand by hand with each hand settled on its own. Many families instead keep a running total and play to an agreed number, such as 500. Either is fine — it changes bookkeeping, not the rules of play.
Can a meld have more than four cards?
A set stops at four — there are only four cards of each rank. A run can be as long as you can build it, up to the whole suit.
Can I lay off on my own melds as well as other people's?
Yes. Any meld showing on the table can be built on, whoever laid it down.
Can I take back a meld once it is down?
No. Once a card is melded or laid off, it stays on the table for the rest of the hand.
What if I go out by discarding my last card?
That is the normal way most hands end. The special no-discard finish is only for when your whole remaining hand melds at once.
Is Rummy the same as Gin Rummy?
No. They are close cousins — both build sets and runs — but Gin Rummy is a two-player game with knocking and deadwood scoring, and it has its own page here.
Source: Bicycle Cards, "Rummy (Rum)" — bicyclecards.com/how-to-play/rummy-rum/ — read in full and rewritten in our own plain words.