If you already know someone in a server, they can invite you. If you have a message history with them, they can right-click your name, click Invite To Server, then select the server to invite you to. This only works if they have permissions to invite you to that server, of course.
Server listing sites like Discord Me are a great way to discover new servers to join. Speaking for Discord Me, things like tags and categories allow for easy searching. If you want to find a server all about anime, you'll have no problem finding all of our anime-tagged servers!
Discord also features its own Server Discovery section, which shows official servers for games and some communities.
