The puzzle is 'easy'....if you've played previous cRPGs on the Infinity engine.
To start with, you have to recognize that when there are green squares those are points of interest. Also, look for mechanics that the game is introducing...like crawling through holes in the wall.
Next, you have to actually read the books that you find in the area or the preceding area, namely the Adventurer's Journal. One of the journals gives you the instructions to solve the puzzle, you just have to figure out the word play and the mechanics.
Word Play: Find the 'stairs'. This is the large gear like object on the wall (with a green square in-front of it) that has a squiggle line on it (which looks like a set of stairs on its side). Then it gives you directions like "go down, then up". This means activating the gear on the wall with symbol of the 'up' arrow, then activating the gear with the symbol of the 'down' arrow, etc. If you press the correct gear, you will get a small cutscene and the symbol will light up on the central floor piece. After the final step, you will be teleported to the next part of the map.
Mechanics: To activate a gear, you have to have your entire party in the green square in-front of the particular gear piece. Additionally, if you mess up the order you can reset the puzzle by returning to the main room and placing 1 party member on each of the 4 buttons. Lastly, there are two mechanics for moving between rooms:
1. Throughout the area there are raised panels on the ground. When a character steps on them, there will be a voice line and you'll hear a door open. Look around the map to see which door opened. You have to leave the party member on the button to keep the door open while you move the rest of your party through. On the other side there will typically be something you can interact with (press Alt key to see it) which then opens a hole in a wall that the button-presser can move through to join the main party.
2. The holes in the wall are just like the ones in the tutorial mission, and once opened, you can freely move the party around.