Conduction band offset is by definition the difference in the electron affinity of the two materials. That is Delta Ec= X2-X1, where X2 and X1 are the electron affinities of the two materials 2 and 1.
The electron affinity is the X= Evac - Ec where Evac is the vacuum free electron level and Ec is the conduction band edge.
The best way to measure the quantities is as to define them.
Sir, an approximate method is to calculate the work functions of both materials and then align the VBs and CBs of both material in same scale. Though this should not be exact as a approximation of equivalence materials behaviour while seperated and together is there.