Big Gun EME contacts are relatively easy. What a good EME'r with a lower performance system will do is set up scheduled contacts with others in the same boat. It takes a lot of time, and listening, and just "trying the water" in EME. Propagation windows can be very brief, but even single-yagi stations can do more than most people think.
Of course most stations are now software-operated, which to me takes out some of the fun but there are enough out there who do it the "old way".