All four of my grandparents emigrated to the US from Greece; does anyone know the steps involved for me to obtain dual Greek-US citizenship?

Ideally get a lawyer to help you. Or be willing to spend a lot of time gathering date.

First, find out where in Greece they emigrated from. Ideally, first look up your father's father. Once you find what Greek municipality he was registered in for military purposes, you will be on the right track. You will also have to get your grandparent's wedding certificates [note that Greece only recognized religious ceremonies before 1982], and your parents' birth certificates, as well as your parents' wedding certificate [ditto on the religious ceremony]. Once you get all that info, you can proceed. If you are a male, and are under 45, you'll also have to provide some other information for military purposes.

The process will take a few years at minimum - but once you complete it, you can also pass on Greek citizenship to your own kids.