Move your car out from under your carport and set up a ladder inside the space. Measure the distance between the ceiling joists or roof trusses that support your carport's roof using a tape measure.
Cut wood slats to lengths that will run from the center of one ceiling joist or truss to the center of another, using a miter saw and miter box to make 90-degree cuts.
Climb the ladder and nail the first slat to the ceiling joist or roof truss with a hammer and 2-inch galvanized nail. Hammer in one additional nail at each truss or joist the slat passes perpendicularly, including a final nail where the end of the slat meets a truss or joist.
Repeat Step 3 to add additional slats to the ceiling. Vary their length or alternate colors and finishes to create the ceiling design you want.
Open a roll of batt insulation. Cut the insulation into sections with a utility knife and insert them into the space between ceiling slats and the carport roof, into the channels created by the ceiling joists or roof trusses.
Continue to cut and add insulation as you attach more wood slats to the carport ceiling. Finish the ceiling by nailing the final slat into place.