Empty the concrete birdbath of any water. Lift off the basin carefully and dump out the water.
Move the birdbath into a garage, basement, work shed or anywhere else out of the elements where you can repair it and let it cure.
Fill a bucket with warm water and a few squirts of dish detergent. Agitate the water to make it sudsy. Clean loose dirt and residue from the birdbath by scrubbing it with the solution and a scrub brush.
Empty the bucket of dirty water. Refill it with clean water. Dip a clean sponge into the water to rinse dirt and soap from the birdbath. Allow it to dry thoroughly -- ideally overnight.
Mix the two-part epoxy's two parts -- a resin and a hardener -- together on a piece of cardboard, using a wooden craft stick. Mix the two parts gently; vigorous mixing will cause air bubbles.
Apply the epoxy mixture to any cracks with the wooden stick. For a broken area, apply epoxy with the wooden stick where the broken pieces meet. Join the two pieces and hold them together, applying pressure until the bond is made. Remove any excess epoxy with a clean rag.
Let the epoxy cure for at least 24 hours before returning the birdbath to its outdoor location.