Summarize:

Citrus removes tacky grease from surfaces. Mix the paste, smear on the pan, let it dry, and rub it with a cloth until the stains are gone. The paste type usually leaves a protective film on the surface after cleaning, but there are many excellent liquids that will clean with no rubbing on your part.
If your copper pans are lined with stainless steel, use the directions for cleaning stainless for the interior of the pans. Clean the outside of the pan with a good grease-cutting cleanser, such as a citrus-based product. After removing the tacky grease from the pans, use a paste made of dish soap mixed with scouring powder (such as Comet, Zud, or Ajax) to clean off hard deposits. Finally, use a copper cleaner, such as the paste type.