Wood stains darken the colour of your wood, as opposed to paints that cover your wood with a coloured film. Many homeowners choose to stain wood instead of paint it because the stain allows the natural grain of the wood to show through. While the process of applying stain is mostly same regardless of the wood's purpose, staining a staircase is a little tricky -- you need access to the steps to apply the stain, without ruining the areas that are drying.
Tape off any areas adjacent to the stairs that you don't want to be stained, using painter's tape.
Sand off any substance stuck to the stairs, using 80-grit sandpaper. Anything stuck to the wood will prevent the stain from soaking in.
Sand the entire staircase with the 200-grit sandpaper. Wipe down the stairs with your tack rag.
Open the can of stain and stir the contents. Mix the stain regularly throughout the staining process to ensure it stays an even colour.
Place your brush into the stain. Apply the stain to the first step, using smooth strokes that go with the grain of the wood. Once stain covers the whole step, remove excess stain by wiping the surface with a rag, using a few smooth motions.
Repeat the staining process on every other step, going all the way up the staircase. This lets you use the staircase -- albeit carefully -- while the stain is drying on the alternate steps. You won't stain the remaining steps until later.
Wait until the stain is dry, according to the directions on the can of stain. This can take up to 24 hours.
Apply another coat of stain, if a darker colour is desired. Let the stain dry.
Open your can of varnish and apply a layer with your brush. Wait for the layer of varnish to dry, according to the directions on the can.
Sand the stained and varnished stairs lightly with 200-grit sandpaper. Apply a second coat of varnish and let it dry. Continue the sanding and varnishing process, applying up to four coats of varnish, depending on your preference. Let the last coat of varnish dry thoroughly.
Start the staining and varnishing process again, this time on the stairs you skipped.