The "how-to-implement" can all be found by following the link, but below is just some extra commentary that I felt would've crowded the AddOn page and it was suggested I could put this here.
LibTutorial is pretty much what it says on the tin. It's a library that provides options for displaying tutorials (though you don't have to limit the use of the displays to the purpose of tutorials) to users in the formats already displayed in-game. (There's the beginnings of room for expansions though). Because it's based on the original game tutorials they should all work for Gamepad mode too, except maybe the Pointer Box.
You can use it to display tutorials about AddOn features or functions as you introduce them to users, (e.g. they open a new menu, display a HudInfo tutorial fade-in/out with details), or use the Tutorial Sequences to run a user through your many options in a LibAddonMenu panel. You could even theoretically throw up tutorials that you code to trigger on combat events or in-game events. Want a simple fade-in/out notification that certain world events are active in a zone? You can do that too! Be creative!
Notes on how to set it up are on the AddOn page, and if you're curious you can look at the Demo.lua file included in the lib to see examples as well (or check out the screenshots on the AddOn page).
Play around, get creative, and let me know in PM or in the comments sections if you have any questions!