This coffered ceiling may look complicated, but with simple lightweight supports and a little planning, it was done in just three days.
One myth about coffered ceilings is that the network of beams that create them has to be attached to a continuous solid frame bolted to the joists. Instead of spending days building an elaborate grid of framing, I attach the beams (faux beams, actually) to U-shaped supports, glued and nailed strategically and intermittently to the ceiling plane, as shown in the drawing.
I assemble the supports in three configurations: straight sections at midspan in larger coffers; cross-shaped at the intersection of two beams; and T-shaped at the intersection of the ceiling and the walls and where one beam ends at another.
I make the supports from inexpensive finger-jointed stock because it's easy to work with, and it nails and glues well. Avoid the temptation to use medium-density fiberboard (MDF) or plywood because these materials are heavy and tend to split when edge-nailed. I allow up to 24 in. between supports. If the distance between them is greater than that, I install a straight section as midspan support. The key is that support for the beams does not have to be continuous, which makes it lighter and easier to keep in a straight line than solid lumber.