An Introduction to Dungeons & Dragons
D&D, in two words, is Collaborative Storytelling. It's known as a Pencil & Paper Tabletop Role-Playing Game (TTRPG). The Dungeon Master (DM), sometimes called the Game Master (GM), is the person who conveys information about a world - environment, characters and dialogue, creature actions, and sensory details - to the rest of the players, who all control a character (Player Character, or PC) who exists in the world the Dungeon Master is describing. The characters in the world the DM/GM creates are known as Non-Player Characters, or NPCs.
The players and their characters have free will, plus a set of abilities their characters can do based on their chosen Class. A PC might be a magic-slinging Wizard, a brawny Fighter, a sneaky and crafty Rogue, a wise and supportive Cleric, or maybe a charming Bard, among many other choices. The set of abilities, as well as a set of numbers for tracking Health and other attributes are recorded on a Character Sheet. As the players declare their intended actions, the DM determines the consequences of those actions in the context of their world.
The game is usually played episodically, with multiple sessions of gameplay so that a complex story can unfold. These are called campaigns. When a DM wants to run a single game session as a discrete one-off adventure, these are called one-shots. When a DM runs an adventure in a world they've created, it's considered a "homebrew" campaign. DMs may also choose to run an adventure from a published source book. Game sessions can last anywhere from half an hour to the entire day, and a campaign can last anywhere from 2 to hundreds of sessions. Average sessions have 3-7 players, and usually last around 3 to 5 hours.
You don't win D&D. You aren't competing against the other players for a prize, instead working together as a cohesive group, or party, to tackle challenges and interact with the world presented by the DM. Having fun and making friends means you're winning D&D!
Articles You Should Read
Videos You Should Watch
Recommended Starter Materials
Disclaimer: You don't need to buy anything, as the basic rules are free.
You may want to purchase a Player's Handbook and a set (or two) of polyhedral dice. For expanded character options, get Xanathar's Guide to Everything. Check out the Dice of Rolling set if you want to start with enough dice for a spell caster.
Playing the game
The Core Mechanic of the Game
The DM gives leading information about something in the world, and the players describe how they wish to interact with the world in response. Then, the DM may request that a player roll a 20-sided die, or d20, to determine the level of success or failure of their actions, adding modifiers based on relevant numbers on their character sheet. If the resulting number meets or surpasses a target number (Difficulty Check, or DC), then the player's character succeeds in their action.
These rolls have a few names: Checks (for performing some action), Saves (to prevent some negative effect), Attack Rolls (where the DC is the enemy's Armor Class, or AC), and Initiative (technically a check, though it has the unique purpose of determining turn order in combat as well as tense situations where split-second decisions may influence the outcome). Some situations and abilities may grant Advantage on a roll, and some may cause Disadvantage. This means you roll two d20s, and take the better (with advantage) or worse (with disadvantage) roll.
When making attack rolls, rolling a 1 (critical failure) on the d20 means you miss, and a 20 (critical hit) means you hit, guaranteed! Per the 5th edition Rules As Written (RAW), there are no other detriments from rolling the lowest number on the die, but many DMs choose to apply dramatic effects when these are rolled. When a 20 is rolled, however, you deal more damage! The pool of dice you have in the description of the Damage for the attack you just rolled for doubles in size and you roll all of those dice at once! For example, a short sword that normally deals one 6-sided die of damage deals two 6-sided dice of damage on that critical hit.
If you want more detail (with examples!), check out this handy article.