As you've learned from the "General information" chapter, entering the Courtyard area is a little tricky. You first need to acquire an invitation, a special boss-related item that allows you to venture to the area. You can enter it only once per invitation - after leaving the area, you will need another invitation to re-enter it. The acquisition of the invitation is related to the Infestation level of your city. That can be checked in the upper left corner of the screen of your "embark screen". You need to complete normal dungeon runs in order to increase the Infestation to Low, Medium and finally to High. The one you're interested in is the last one - High.
Once it reaches that state, you will, from time to time, encounter a new enemy (accompanied by other Courtyard-area mobs) called the Gatekeeper. This is a variation of a foe that you've probably fought before. Once killed, the Gatekeeper will drop one invitation to the Courtyard. This enemy can be found multiple times after reaching the High level of the Infestation, allowing you to "grind" invitations and enter the Courtyard area many times. The isn't any restriction to the area where you can meet the Gatekeeper, although it seems that he spawns more often in the Weald and Barrens areas.
Keep in mind that once you've killed the boss related to the quest (Baron, Viscount, Countess), the Infestation level will revert back to Low. When that happens, you will need to increase it back to High and fight the mentioned enemies to get another invitations to the Courtyard.