How can I correct an expected climb rate for density altitude?
That depends on what the POH for your specific aircraft includes. For example the POH for the PA-28 Warrior has a correction chart for calculating just that. In this case you need to use pressure altitude and local temperature (which combine to density altitude anyway).



Its important to use the POH for the specific aircraft as things like engine modifications, installed propellors and other changes to the airframe can greatly affect the numbers. These changes may only be reflected in the POH for the airframe its self and a copy found elsewhere may be inaccurate. Correction charts and your POH may also include pertinent information about operational limitations during a climb as well.