Wipe all surfaces of the chair clean with a damp rag. Pay particular attention to corners and joints, where dust and other debris are more likely to gather. Allow the chair to air dry.
Squeeze a generous amount of stain directly onto the chair. Paint it into the surface with a foam brush -- you can either paint with the grain or apply the stain in circular motions. Alternatively, you can use a soft cloth or a lamb's wool applicator to spread the stain.
Wipe the chair down with a clean, dry rag. The idea here is to soak up as much of the excess stain as possible. Again, you must wipe with the grain of the wood. Otherwise, you run the risk of streaking.
Wipe the chair down until no more stain lifts up from the wood. The chair should feel almost dry. If necessary, use additional cloths if the one you are using becomes saturated.
Allow the stain to dry completely. This varies by manufacturer, so check your product's label for specific wait times. Note that humidity also plays a factor into the amount of time you have to wait between coats.
Apply another coat of gel stain if you want a deeper color. Repeat until you are satisfied with the appearance of the chair.
Check the label for instructions on adding a protective topcoat. Some manufacturers combine a varnish with the gel stain so you do not have to apply additional sealers. If yours is not a combination gel stain and varnish product, you will need to paint on a polyurethane sealer or varnish. Allow the topcoat to dry completely.