Tray aka trey ceiling is under a gabled roof, a horizontal ceiling constructed part of the way up toward the ridge.
Common question is that how do you frame a tray aka trey ceiling?
Determine how large of a 45 degree angle you wish to have where your walls meet your ceiling. Cut an appropriate number of 2x4s with a 45 degree angle on both sides all the same length. Its nice if you can place these 16" on center, but 2' on center is acceptable. Hold one in place at each corner of the room and make pencil line on the wall at the bottom tip of the 2x4. Snap a chalk line on the wall between the pencil lines.
You can do the same thing on the ceiling if you wish. follow these lines and you'll wind up with a straight ceiling. Make sure you attatch these 2x4s straight up and down to a wall stud and the corrusponding ceiling joist or truss. It gets complicated when you get to a corner. You need to establish a " ridge beam" from the chalk lines that meet in the corner on the wall to your 2x4s that meet on the ceiling. this will require 4 compound miter cuts. comtinue running the 2x4s on layout into the corner but instead, connect them from the wall to the newly established "ridge beam" these will also require a compound miter on one end.
Then have a sheet rock party. If the corners sound too intimidating, do every thing else and call in a pro to finish the corners. at least you'll save money anyway. Make sure the pro is aware of your plan on how you're going to install the tray ceiling before you begin, he may have additional bracing or a different way all together. Hate to have all your work wasted. Hope this gives you somewhat of an idea