Find and remove the screws under the railing going into the post. The first newel post comes off, and the balusters up to the next post come out easily. After the last baluster is removed, the railing on the stairs comes right off.
At the second newel post, you'll need an extension on the drill to reach the screws holding it in place. If the screw head is broken off in the hole, use a reciprocating saw to cut right through it. The second post comes out and you can now remove the remaining balusters.
Now the carpet needs to come out. Use a utility knife to cut the carpet and some pliers to get a good grip. At the edge along the steps, a hammer and a cold chisel help in removing the tackless strips. Continue up the steps pulling the carpet loose. It's just a matter of getting the right start. Once you get the edge going, it comes right off.
The landing piece comes off in one big piece. Remove the carpet pad and the tackless strips on the landing. Just use a pry bar to get under the strips. Nothing will have to be done to the sub-floor on the landing because the new hardwood flooring will go right on top of it.
Remove the frame that the carpet attaches to, along the side of the steps.
Slip the pry bar under the top tread and pull it up. Note that removing treads is hard work because not only are they nailed down, but they're glued down as well. Some of the risers will come off with the treads. The last one has to be busted to come out.
Note: Be sure to keep the damage to the drywall along the stairs to a minimum. The new skirt boards will cover everything as long as you don't get too carried away.
Sand the treads, railing and newel posts with 220-grit sandpaper, making sure to sand with the grain. Once everything is lightly sanded over, wipe them clean with a rag. Just dip a clean rag into the stain and spread it evenly over the wood, starting with the treads, followed by the railing and newel posts.
Since the new risers, balusters and skirt boards need to be painted, go ahead and sand and paint all of them while you're in paint-and-stain mode. Also, painting many of these pieces before they are installed is much easier.
When the stained parts have dried, apply a coat of polyurethane on them. Use a quality brush, and always follow the grain. Also apply polyurethane to the treads, railing and posts.
Always be sure to stir the polyurethane with a stick. You never want to shake the can because it creates bubbles that you will brush on to the wood.