Spread a blanket or large tarp over the floor to protect the coffee table's surface from scratching.
Turn the table over on the blanket or tarp to inspect its joinery.
Examine the joint type. Braced table joinery means that the legs are attached to the table's frame with metal or wood corner braces joined with screws. Bolted legs screw into a threaded piece that sinks into a wood block. Mortise-and-tenon joints have wood dowels or rectangular wood pieces that fit into a hollow section with glue holding them in place.
Back the screws out of the corner braces holding the legs in place with a screwdriver.
Pull the legs out of the holes. If the legs are difficult to remove, glue might be holding them in place. Grip a table leg as near to the underside of the table as possible with an adjustable pipe wrench and twist to remove the leg.
Clean old adhesive or bits of wood out of the hole with 220-grit sandpaper.
Apply wood glue to the top of a commercially available table leg. A standard dining table stands 30 inches tall from floor to tabletop. Measure the thickness of the table top and subtract that number from 30 inches to determine the length of the table leg needed.
Fit the table leg into the hole. Insert screws through the brace and into the leg. Tighten the screws with a screwdriver. Wipe up glue from around the leg with a damp rag. Repeat for each table leg.
Turn a table leg counterclockwise to loosen and remove it from the underside of the coffee table.
Position a commercially available table leg with a protruding screw over the sunken threads found on the underside of the table. Subtract the thickness of the table top from 30 inches to find the length of the table leg.
Turn the leg clockwise to tighten it in place. Repeat for each table leg.
Grip the table leg as close to the underside of the table top as possible with an adjustable pipe wrench. Twist the leg forcefully to loosen and remove it. If a square or rectangular mortise-and-tenon hold the leg in place, position a chisel at the seam of the leg and underside of the table. Strike the chisel with a mallet to cut the leg out of the mortise. Chisel out remaining pieces of the tenon.
Use 220-grit sandpaper to sand old wood glue out of the mortise.
Apply wood glue to the tenon or dowel end of a commercially available table leg and insert it into the holes. If the new table legs do not have a dowel joint, drill a hole in the same size as the dowel removed 2 inches deep in the center of the table leg with a power drill. Apply wood glue to a 2-inch section of a 3-inch long dowel. Tap the glued end of the dowel into the hole to create a dowel-jointed leg. Subtract the thickness of the table top from 30-inches to determine the leg length.
Place a hand-screw clamp over the new joinery and tighten it to hold the leg in place.