Getting an in-game invite into the D3 clan is the same process as always for ALL General Games, you should submit an invite request by visiting and posting an invite request in this forum which also contains instructions:
General Games’ In-Game Invites Forum
Then check this forum for in-game contact people who can do invites:
General Games Info And Chain Of Command
Typically one of the contact people in the above list will see your post in the above thread and help with any in-game coordination with the invitee needs to happen.