It's far easier to drywall a garage before the garage door is installed. You can't simply move a garage door's metal hardware out of the way because the large metal springs have tension. Trying to remove them can cause serious injury if you don't know what you're doing. The only solution is to install the drywall so that it butts up against the hardware, then fill in the gaps. Check your local building code to verify that your drywall is the correct thickness. Typically, building codes require 5/8-inch drywall because of its resistance to fire.
Things You'll Need
Halogen lights (optional)
Spray foam insulation
6-inch drywall knife
Lower the garage door. Lock it so that nobody opens it while you are working. If the garage is dark without the door open, set up some halogen lights.
Install drywall around the garage door support brackets. To do this, attach the drywall to the ceiling studs with drywall screws every four to six inches. Hang the largest pieces of drywall first, then the smaller ones. The goal is to install all the drywall that you can fit easily, but don't worry if you have to leave a few gaps near the metal hardware. This is typical.
Fill the gaps around the metal brackets with spray foam insulation. Most local building codes require that you completely fill every gap in a garage ceiling in order to contain potential fires. If it's not covered by drywall, it has to be filled.
Trim any spray foam insulation that expanded out of the gaps with a utility knife. Leave the foam flush with the surface of the drywall.
Cover over the sites where you sprayed insulation with joint compound in order to hide them. Use a six-inch drywall knife to completely coat the areas. Allow the areas to dry, then smooth them with 100-grit sandpaper.
Hang the drywall in the rest of the garage as normal. Measure and cut the sheet rock to size, then attach it to the studs with drywall screws.
The edges and corners of the garage-door support brackets are sharp. Move slowly and watch your head.
Rent a scaffold to save time. Make sure it has wheels so that you can roll it from one location to another.