Lengthening a chair leg -- or all four -- can make an old chair usable again or raise a chair to a better height, such as for seating at a table or desk. When doing woodworking of this sort, be sure to always measure twice before cutting, wear safety glasses and earplugs, and keep children and pets out of the way while you're working.
Place the chair on a workbench or table so that you have good access to the leg you need to lengthen. Clean off the chair leg with water and oil soap to remove any dirt, grime or old glue. Thoroughly dry the leg with a dry, soft, lint-free cloth.
Measure the dowel that matches the diameter of the chair leg and mark how long of a piece you need to add to the existing chair leg. Measure again and make a mark on the other side of the dowel then connect the marks so that they are equal.
Saw through the dowel at the marks and sand the rough edges of the piece you've just cut. Pre-drill two holes, one going into the bottom of the chair leg and one going into a flat end of the dowel.
Screw a double-headed wood screw halfway into the chair leg. Apply a small amount of wood glue around the screw then, with the dowel straight in line with the chair leg, screw the dowel onto the other end of the double-headed screw. Do not over-tighten the screw, just make it hand-tight. Place the joint in a V-channel vise and allow the wood glue to dry. Scrape off any dried glue outside of the joint and sand and polish or paint the leg.