Most domains can be unlocked simply by going to it and interacting with the door, but there are some that can be tricky and confusing to unlock.
Taishan Mansion in Jueyun Karst
Taishan Mansion domain is located in Jueyun Karst. You can go there pretty quickly by going to the teleporter near it, and walk/glide a short distance.
To lower the water level, start by activating the device near the temple. There will be monsters here that you need to clear out.
Once the device has activated, go to the center area and destroy the glowing rocks. You will get a light orb that follows you around. Walk to the lanterns to light them up. You need to light all 3 to open the seal for the device in the middle.
Hidden Palace of Guizang Formula in Luhua Pool
Hidden Palace of Guizang Formula is located in Luhua Pool, in the center of the circle. You can reach it pretty quickly from the nearby teleporter. Make sure to bring a fire element character.
Once you're there, you will need to light up the fire pillars in an order. Light the ones with the broken bridge behind them with the order of middle, right, and left from this picture.
Hidden Palace of Zhou Formula in Wuwang Hill
Hidden Palace of Zhou Formula is located in Wuwang Hill, deep in the dark forest. Make sure to bring a fire, and a geo character. You can bring the main character for the Geo element by interacting with the Statue of the Seven - Geo using the main character.
In order to unlock the Geo pillar, you will need to light up the small fire torches nearby. Start with the one close to it.
The next ones are guided by the floating flames in the air. Go to the west of the Geo pillar and climb up a little. There will be a small temple. There are two small torches next to it, on the left and the right.
You might also need to light the one behind the rock near the Geo pillar as well. Once all the fire pillars are lit, the seal for the Geo pillar will unlock, then simply activate it with a Geo elemental attack.