Of course, we can't talk TTRPGs without talking about Dungeons & Dragons (D&D). Created in the 1970s, the game has grown and changed over time, reflected through the different editions of the game published. The current edition is 5th, but that doesn't mean people can't play the older editions. Each has its appeal (to a certain degree, some changes over time have made the game just easier to play and includes fewer hurtful stereotypes), though personally I prefer 5th edition. With each edition, D&D publishes supplemental books to help players and DMs, like the Monster Manual and the Dungeon Master's Guide, as well as adventures DMs can run for their players. These aren't required in order to play, but can help guide DMs and players in their games and make it easier for newer DMs to jump into a campaign without creating everything from scratch.
In D&D, players choose a race (what kind of being are you: human, elf, dwarf, gnome, etc), class (what do you do: bard, fighter, rogue, cleric, wizard, etc), background (where did you come from: acolyte, charlatan, courtier, artisan, etc), and equipment (what you wear: armor, weapons, magical tools and supplies, food, etc) at start of play. They may have talked beforehand with their DM about what they wanted to play, may be getting help from other players to build their character, or may be making the character completely during the first session. Depending on where the game is set (there are a huge number of locations in the D&D world where a game can be set, and of course groups can make up their own settings too) might affect what their choose for their characters, such as the difference between playing a game in a desert vs on a boat.
For DMs, a game of D&D generally involves preparing a scenario for the players to interact in, which can include making non-player characters (NPCs), making or printing maps, picking/creating monsters or other bad guys for the players to fight, and writing the general plot of what the players can do/find out. This isn't how all DMs run games, though. Some go all out, to the point of costumes, lighting, and character voices. Others prefer to improvise and see what the players do, then react to that, with only a general plan of what's going on. D&D doesn't work super well with this style of DMing (I'll go into other games this does go quite well with in the next tab), but it certainly can be done. Still other DMs prefer to run the pre-written campaigns that D&D publishes rather than creating their own content. All of these are valid approaches! It might take some trial and error to see what approach works best for your DMing style.
Here are just some of the D&D books available in the SAPL catalog; try searching 'dungeons and dragons' in the catalog to see how many we really have! They vary from source books for earlier editions all the up to the current 5th edition to introduction books for younger players, supplemental books with more options for players and settings for games, and full adventures for DMs to lead their players through. Checking library copies out is a great way to learn about the game without having to dedicate money, and can be a cost-effective way to play as well.