Measure the outer dimensions, both length and width, of a rectangular vertical HVAC duct around its widest part, at a place where two sections of duct join in a seam. Or measure the diameter of a round HVAC duct, which should be close to a typically duct width of 6, 8 or 10 inches. Add 1/8 inch to the width and length, or to the diameter, to allow for wrapping with fiberglass insulation.
Add additional space for the sized chase if it will also contain an adjacent pipe, drain or wiring.
Stack two pieces of scrap 2-by-4 blocks on the floor. Measure the height from the ceiling joist to the top of the blocks, which accounts for the thickness of the sole and top plates. If you can fit the top plate between the joists, use just one scrap block to attain this measurement, which tells you how to size the studs.
Mark down the sizing information and make final determinations of the amount of 2-by-4 lumber needed. Allow enough to make a bottom plate on the floor -- essentially a rectangle of butt-jointed 2-by-4s -- with an inside dimension equal to the figures obtained in Step 1. Calculate additional lumber to make an identical top plate to fit between or just under the ceiling joists.
Size studs for each of the four corners of the chase to run from the top to the bottom plate. Complete the sizing with crosspieces halfway between the bottom and top plates and between the studs directly underneath the top plate.