  F\"orster resonances provide a highly flexible tool to tune both the strength
and the angular shape of interactions between two Rydberg atoms. We give a
detailed explanation about how F\"orster resonances can be found by searching
through a large range of possible quantum number combinations. We apply our
search method to $SS$, $SD$ and $DD$ pair states of $^{87}$Rb with principal
quantum numbers from 30 to 100, taking into account the fine structure
splitting of the Rydberg states. We find various strong resonances between
atoms with a large difference in principal quantum numbers. We quantify the
strength of these resonances by introducing a figure of merit $\tilde C_3$
which is independent of the magnetic quantum numbers and geometry to classify
the resonances by interaction strength. We further predict to what extent
excitation exchange is possible on different resonances and point out
limitations of the coherent hopping process. Finally, we discuss the angular
dependence of the dipole-dipole interaction and its tunability near resonances.
