Running a game of Dungeons & Dragons requires very little, but these three are the foundation to a campaign:
a Character, which the players use to act out roleplay and combat
a Dungeon Master, who guides the party through a series of events
and a Story, which both the Players and Dungeon Master work together to create
With this in mind, there are a few tools that both players and dungeon masters use to help the campaign move forward. These include maps, tokens, and other items which are not required to play the game, but the most essential of tools are Character Sheets and Dice.
Character Sheets are pages of information regarding a character's build. This includes everything from character creation, as well as backstory, inventory, and spell sheets if needed. These can be physical copies, or digitized in either a PDF or in a Virtual Tabletop. Players may utilize a custom character sheet for their information, or use the Standard Character Sheet provided by Wizards of the Coast.
Dice are utilized for rolling things such as Skills, Attacks, Saving Throws, and many other facets determined by character builds and situations. There are 7 basic types of dice that are used: the D4, D6, D8, D10, D12, D20, and D100. Custom dice, such as D2 and modified D100, can be utilized for special occasions, but these base 7 are the most important to play the game. Virtual versions of dice are available for use, such as Google's Virtual Dice Roller and DDDice.
While playing in a campaign, Dungeon Masters and Players can interact with each other through a series of Encounters. Encounters are interactions between Players and Non-Player Characters (or NPCs) through either Combat or Roleplay.
Characters are made up of three main parts: Race, Class, Background. Race makes up a character's initial attributes, such as abilities and Ability Scores. Class determines a character's skills, as well as how the character develops throughout the game. Background defines how a character behaves, and includes features such as Flaws and Ideals. These lay the groundwork for creating a character for any given campaign.
There are several different option to choose from when creating a character, with each new source book introducing new material for both players and dungeon masters. These are the options for the most base version of the game:
Races: Dragonborn, Dwarf, Elf, Gnome, Half-Elf, Halfling, Half-Orc, Human, and Tiefling
Classes: Barbarian, Bard, Cleric, Druid, Fighter, Monk, Paladin, Ranger, Rogue, Sorcerer, Warlock, and Wizard
Backgrounds: Acolyte, Spy/Criminal, Folk Hero, Noble, Sage, and Soldier
What your character starts with as far as their abilities is dependent on the campaign's Starting Level.
Different sources give access to a multitude of other options. For example, Eberron: Rising from the Last War gives players access to the Artificer Class, while Dragonlance: Shadow of the Dragon Queen adds the Kendar as a Race option. There is also a special option called Homebrew, where players and dungeon masters create custom content that is considered official. Players and dungeon masters can create their own Homebrew content, or they can utilize content shared online by other players.
Once these three have been chosen, players are given options of Attributes to choose from based on their choices. These make up the majority of information on the Character Sheet, and include Ability Scores, Saving Throws, Skills, and Proficiencies.
Aside from Ability Scores, each option will determine what the character can add their Proficiency Bonus to. The Proficiency Bonus is a number determined by the character's overall level, which is added to rolls the player is proficient in. If a character is not proficient in a roll, then the roll only adds the Ability Score Modifier associated with that trait (or in the case of Proficiencies, the roll would be a straight roll).
The character's background determines the Characteristics options players may choose from, including Personality Traits, Ideals, Bonds, and Flaws. Players may also use the background to help determine the character's Backstory. The Backstory is the story of the character's life before the campaign takes place. It is entirely dependent on the character's information, campaign setting, and player's creativity.
With the character sheet fully fleshed out, you're ready to begin your first Dungeons and Dragons adventure.
The role of the Dungeon Master is to guide players through the fantasy setting in which the Campaign takes place. The Campaign is the story which the Dungeon Master and Players create together through a series of Encounters, and it takes place over any number of sittings referred to as Sessions.
A Session is a period of real life time that Dungeon Masters and Players actively participate in the game. The first session of a campaign is usually one where the campaign setting is described, characters are fleshed out, and rules are explained. Since the campaign itself doesn't start during this session, it's commonly referred to as Session 0. Sessions can last any amount of time the Dungeon Master and Players are comfortable with, and can happen anywhere between once a week to once a month depending on schedules. The exception to this is One Shots, which are campaigns designed to only last for one extended session.
Each interaction can be summarized as this: The Player attempts to do something, the Dungeon Master describes what happens. Throughout the campaign, the Dungeon Master is tasked with two roles: Narrator and Referee. As the Narrator, the Dungeon Master must describe the environment and characters in which the Players interact with. As Referee, the Dungeon Master determines how Players decisions will play out.
When deciding to run a campaign, there are two options to choose from as far as setting: Premade or Homebrew. Premade campaigns are ones that have been designed for Dungeon Masters to run without having to create it from scratch. This includes official campaigns published by Wizards of the Coast, or homebrew campaigns that have been published online for other Dungeon Masters to use. Premade campaigns are easier, as it reduces the amount of planning on the Dungeon Master's part, but also somewhat restricts them on creativity. Homebrew campaigns are ones which the Dungeon Master creates from scratch, using their own world for the setting and creating every element that goes into it. Homebrew campaigns encourage creativity, as Dungeon Masters aren't confined to the settings of a premade campaign, but it also makes it to where the Dungeon Master must put an extensive amount of effort into planning.
As Dungeon Master, there is one more tool that is vital to have: a Notebook. Dungeon Masters have to keep track of NPCs, locations, items, quests, and many other details that may affect the players or the campaign. Be it physical pen and paper, or apps such as Notion or Google Drive, it is important to have some form of note-taking tool in order to keep information in.
Regardless of which format you choose, it is important to always remember it is just as important for the Dungeon Master to have fun as it is for the Players.