Wet Down Chair
Using a clean sponge soaked in hot water, wipe down the chair legs before sanding. This causes the fibers of the wood to swell and stick out, almost like whiskers. When you begin to sand, the whiskers will be cut off cleanly. Doing this will result in a smoother sand, and will also allow the stain to spread evenly, if you plan on staining the chair legs later.
After you've let the chair dry (usually a few hours), begin to sand the legs using a steel wool sanding patch, which can be found at any hardware store. Sand with the grain of the wood, as going against the grain can result in very noticeable scratches. Begin on the inside of the legs and sand from top to bottom in long, even strokes. Use firm pressure to ensure a clean finish. Take your time, but don't worry about all the nooks and crannies at this point.
When you've finished sanding all the legs, you'll probably still need to get into the tiny grooves and details. The best way to get into these nooks and crannies it to use a piece of jute twine, also sold at hardware stores. Cut the twine into about a 6-inch-long piece and wrap it around the small area you wish to sand. Take an end in each hand and pull the twine back and forth, which will smooth and sand the grooves.