Find the broken reeds of the wicker. Snip through the broken reeds at either end with sharp scissors and carefully remove them. Apply a dab of wood glue to the remaining stubs of the reeds to keep them from splitting and allow it to dry.
Fill a large container with water. Place the new reeds in the water, rearranging them as necessary so they are completely covered. Let the new reeds soak for 30 to 45 minutes.
Remove the reeds from the water and test them to make sure that they bend back and forth easily. Glue one end of the new reed to the underside of the old wicker near the area to be repaired. Hold the reed in place for a few minutes until the end is secure.
Weave the new reed into the old wicker following the original pattern. If you come to the end of one reed before the repair is completed, attach the end to the underside of the wicker with a dot of glue and begin a new one. End the repair on the underside of the wicker and secure the final end with more wood glue.
Let the glue dry completely. Paint or stain the new wicker as necessary to match the rest of the piece. Apply a clear spray varnish once the paint has dried to protect the piece from the elements.