Frame around ducts that run along exterior walls by building the wall around them. Lay the wall's bottom plate on the floor in front of the ducts, marking where each duct is. Cut a notch out of the plate in each duct location, far enough in so the bottom plate can slide around the duct and meet the outside wall behind it. Alternatively, if you have the space, just build the wall in front of the ducts, leaving them between the exterior foundation wall and the new framed wall.
Build custom framing to accommodate ducts that run in unusual positions that can't be enclosed within the wall. Screw drywall onto the framing to hide the ducts. Use 2-by-3 lumber, which is adequate for framing that is only for covering a duct.
Move ducts that run across the floor by repositioning them over the ceiling joists and directly down to their destination, then build a wall around them.
Frame a thicker wall with 2-by-6 lumber to save the trouble of constructing many custom frames for large ducts. Situate the 2-by-6 wall so large ducts fit inside the framing and don't conflict with the location of the drywall on the faces of the wall.