Check out the existing garage structure. If the garage is old or not built well, it may need to be shored up before anything can be added above it. Pay particular attention to the foundation, since all of the building's weight is ultimately carried here. Look for cracks in the foundation walls and the concrete floor slab, and for areas where the foundation looks to be sinking or bowing. If you have any doubt that the structure is unsound, consult a certified structural engineer or architect before continuing.
Remove the existing garage roof carefully, so as not to damage the structure below. Start at the ridge of the roof and work down. Order a dumpster for the disposal of rubbish if desired. It is worthwhile to save lumber from the roof framing if possible, since this can be reused later. When the roof has been removed, cover the garage with tarps to keep rain from getting in.
Cover the exposed garage ceiling joists with 3/4-inch plywood. This is the deck upon which the next story will be framed. This method, known as platform framing, or western framing, is the way most wooden structures are now constructed.
Frame new two-by-four exterior walls on the newly constructed plywood deck. Double the top plates and cross lap them at the corners to tie wall sections together. Make sure your walls are plumb before securing them. Build interior partition walls where desired.
Cut a hole in the floor and build a double joist box with double headers at both ends in the ceiling below for the new stairs. Build a staircase either in the opening or on the outside of the garage, if space is limited.
Frame a new roof above the new second floor, using the original framing lumber if possible. Cover the roof framing with 1/2-inch plywood sheathing, and cover that with finish roofing materials. Finish the interior as desired.