Use the manufacturers' instructions to remove the old door. It mainly consists of carefully unlatching the door from the pulley system, then taking apart the panels of the door and unscrewing the tracks. Make sure to remove one panel at a time, or they could all fall in on you.
Measure the various areas where the door will be installed: door-opening height and width, headroom (from top of opening to ceiling), and back room (length of garage). For the headroom, you should have about 10" to 12" of space, depending on the spring system you're installing. For the back room, you should have the door height, plus another 18" or more of space.
With the proper measurements in hand, temporarily attach stops to both sides of the opening and make sure they are flush with the inside edge of the door jamb. Using the sawhorses, lay out the bottom piece of the new door, and attach any weather stripping (if necessary). Additionally, attach any hinges and lift handles to the piece.
Insert the bottom piece into the door frame, and use a level to properly set the piece. Once the piece is in place, tap nails partway into each jamb. Slant or slightly bend the nails to secure them in place. Use the manufacturer's instructions to assemble the vertical, curved and horizontal pieces of the track and set aside.
Install the second panel on top of the first one, hammering nails into the side jambs to hold it place. Install the hinges and repeat the process for however many panels are necessary. You will need to anchor each piece into the door jamb.
Once all the sections are secured, install the rollers in the section's roller supports. With these in place, place the rollers in the assembled track, securing the track's brackets as you go along. Be careful not to have the rollers pressed too tightly against the track because friction can cause damage to the door.
With the vertical tracks secured against the jambs, install the curved and horizontal pieces. When installing the horizontal pieces, use your previous measurements and level to make sure the tracks are straight and that they are pointing away from the opening at 90 degrees.
Now that the tracks are secured, assemble the springs according to the manufacturer's instructions. With the help of a partner, lift the door to about half length to make sure the tracks are level and parallel. Once you're all set, lift the door the remaining distance and attach the springs to the pulley system.