Materials:
Stair tool
Stapler
Hammer
Awl
Carpet knife
Razor knife
Measuring tape
Power stretcher (also known as a "crab stretcher")
Work gloves
Safety glasses

1. Measure and cut a piece of carpet to the appropriate length, and have the edges bound by a professional
2. Mark the location on each step where the runner will rest. Make an inside mark to show where the edges of the padding will extend and an outside mark to show how far the carpet will extend.
3. Cut a piece of padding to fit on each step. Lay each piece in place, and secure it with a hammer stapler. 
4. Roll up the carpet, and lay it a few steps above the bottom. Then pull the end toward the bottom.  You'll need some slack to work with so that you don't tug too hard on the bottom and cause the entire roll to fall down on you. Keep the roll centered as you work your way up the stairs.
5. Run a row of staples along the bottom of the bottom riser where the carpet meets the floor.  The staples will be hidden because they're in a corner.
6. Pull the carpet tight, and run a row of staples along the top of the riser where it meets the tread of the stair.
7. Use the power stretcher (crab stretcher) to pull the carpet tight as you place another row of staples in the corner between the riser and the tread.  
8. Use the stair tool to wedge the carpet into the corner
9. Repeat the process as you work your way up the stairs