Most houses today are built with prefabricated roof trusses, rather than rafters. Trusses are lighter and easier to install at a job site because they are put up as a single unit rather than individual elements. Many garages, however, still use rafters which can provide a bit more storage area because they have fewer internal braces. Raising rafters requires some precise cutting to make sure they fit securely between side walls and a ridge board at the roof peak. It also requires help -- at least three people will be needed.
Cut rafters according to the roof pitch, which is the angle of the slope from wall to peak. They require a "plumb cut" at the top to fasten to a ridge board, and notches at the wall end to fit over and fasten to the cap board on the wall. Rafters can be cut using a framer's square and the tables on it, or by using information from a rafter table, available online or at a building supply store. Cut enough pairs of rafters to place one set every 24 inches over the garage.
Erect one pair of rafters at the back end of the garage, with notches firmly nailed to the wall cap and the plumb-cut ends resting against each other. Use a level to make sure they are plumb. Move to the other end of the garage and erect another pair of rafters, also checking for plumb.
Cut a ridge board the length of the garage, using the same dimension lumber as the rafters. Slide it up under the two end rafter pairs; the pressure of opposing rafters should help hold it in place. (This will require a worker on each set of end rafters and a third, or even a fourth, to lift the ridge board). Check the ridge board with a level to make sure it is level and the ends match the rafters. Nail this in place to the two end rafter pairs.
Move down the roof from starting end to the other end, installing pairs of rafters 24 inches apart. Nail the ends to the wall caps and the tops to the ridge board. Check each rafter pair for plumb before nailing.
Add bracing if needed with 2-by-4-inch gable studs and cross ties. Gable studs are upright boards to fit at the roof ends between the ridge board and the end wall cap. Cross ties are cut to fit horizontally between rafters below the ridge board. All nail into place.