How are DACs integrated in color LCD screens?
From this patent about TFTs:

The pixels are organized in a matrix like this:


and each pixel circuit looks like this:



During operation, voltage levels according to desired brightness levels for each pixel of a single row are put on the vertical lines Cn. After this, a signal on RAm and RBm activates the transistors of all pixels in that row, and the voltage levels Ci are transferred to a capacitor inside the pixel. The transistors are deactivated, and the whole process continues with the next pixel row.

That capacitor not only stores the voltage applied, it also is part of the liquid crystal cell and its electric field causes the crystals to move into the orientation needed for the desired brightness.

Here is also a drawing of the layout of a pixel:



Finally, I have to say I have no idea why there are two transistors, but I also didn't read the full document. The stuff is not as easy as described here, but it's OK to say that both transistors are used to put the voltage level of Cn onto the capacitor.

Now, you only need as many DACs as there are columns, but DACs can be quite simple and small.