I was taught this as a young child by my grandmother. It's how my family plays what we call rummy, but I cannot find anything like it online:
Two plus players (we've played up to 4), all dealt 7 cards. Deck is placed face down and one card turned up, player to the right goes first. They can either pick up the face up card or the top card from the deck, then discard a single card. Next player can either pick up the top card from the discard pile, or the entire discard pile, or a single card from the deck, then discard a single card. Play continues like this.
Players can put down runs of 3 or more and melds of 3 or more at any time during their turn. Following this, a player that has put down a run or a meld of their own can on their turn add to other players runs and melds (keeping them with their own cards, so say player one had 7, 8, 9 and 10 of hearts down... player two as long as they've also go their own run/meld placed down can put down just a jack of hearts, player one could then place down just a queen of hearts, etc.)... you can choose to put down your runs and melds immediately upon getting them or you can hold them and half the deck in your hand (if you keep picking up the discard pile) until you can go out, by having no cards left in your hand. It's up to you. You don't need to give any warnings before going out, and going out does not require discarding a card.
