I think the mostly likely way they found us is the way we are finding exosolar planets now.
We are putting a new telescope at Lagrange Point and turned away from the sun with a shield that will be able to find Earth sized planets. Within about 10 years we will be able to determine if they have an atmosphere and what it is made of.
My guess is their telescopes or sensors saw our Blue Planet hanging in space, sensed the size, mass, atmosphere and came to check it out.
Actually, a race only 200 years ahead of us could teach us a lot if they were so inclined.
