Elephant glue is a type of super glue that contains cyanoacrylate, which dries fast and can be used on wood. Due to its rapid drying time, chair parts cannot be disassembled and reassembled as if you were using wood glue. It's somewhat temporary, depending on the condition of the chair, but for a quick chair back repair you can't beat it. If the chair has broken parts, Elephant glue may not be enough to secure the wobbly back. Use white glue for this purpose.
Remove the cap from a tube of Elephant glue. If the tube is sealed, clip the top off the tube using a pair of diagonal pliers to open a 1/16-inch hole in the end.
Place the chair on a worktable or bench. Pull or push on the back of the chair with your hands to locate loose joints, tenons or dowels. They will most likely be where the dowels or spindles penetrate into the seat, or on top where the top of the chair fastens to the top of the spindles or dowels.
Insert the tip of the tube into any spaces or gaps between dowels, tenons or parts that open up when you pull on the chair back. Inject the glue into the spaces until the glue flushes with the top of the gap. Work fast. Pull or push the chair in the opposite direction. Inject the glue behind, or opposite to, the first application. Do all of the gaps or spaces, pulling and pushing the chair back with your hands in all directions.
Insert three nylon strap clamps under the chair seat spaced evenly. Loop them over the top, insert the end of the strap clamp through the buckle on the back of the clamp and pull the strap tight but don't use force. Just snug it.
Place three bar clamps, evenly spaced on the back of the chair vertically. Place one jaw on top and one jaw under the seat on each clamp. Tighten the clamps snug, but not too tight.
Tighten one strap clamp using a 1/2-inch wrench. There's a nut on the buckle for this purpose. Alternate to one bar clamp, and then back to the next strap clamp. Repeat alternating between the clamps so that the chair back bonds back on the seat evenly. If you notice that the back is tilting to one direction, loosen clamps as needed, and tighten the opposite clamps until the chair back is back to its original position and glue oozes out of the gaps. Allow the glue to dry overnight. Remove the clamps.
Scrape off any residual dried glue using a chisel. If you find visible gaps, mix a small amount of Elephant glue with sawdust. Use the mixture like putty to fill the gaps.