How can beans grow in clay?

Same as in any other soil but there are ways to help. The standard recommendations for improving clay soils are: try to improve drainage, add as much organic stuff as possible, judiciously add lime or calcium, and dig in autumn. A clay soild can form a crust which hardens and can prevent tejh beans breaking through this can be solved by adding a compost layer on top which helps the soil retain moisture and prevent a crust forming.