Remove the old expansion joint material with a hammer and chisel. Hold the pointed end of the chisel at an angle on the old expansion joint. Hit the end of the chisel with the hammer, forcing the pointed end into the material. This will allow you to grab the old expansion material and pull it up away from the joint.
Clean the open expansion joint with the broom to remove the majority of dirt and gravel. Wash the joint thoroughly with a garden hose. The goal is make the joint as clean as possible so the new joint mastic will adhere to the older concrete.
Insert the expansion joint replacement board into the cleaned out joint. Tap the board into place with the hammer. The depth of the new replacement board must at least 1/2 to 3/4 inch below the surface of the concrete.
Trowel the joint mastic into the top of the joint, over the new replacement expansion joint board. Smooth the material so it lies even with the existing concrete surface. Keep all traffic from the mastic material until it fully cures according to the manufacturer's labeling.