What are the two ways that you can determine if a substance is soluble?
As far as I know, there is only the one way whether a substance is soluble. And that is by experiment.
All our ideas on solubility (and of course chemistry and physics in general) are based on experiment. We could list properties of ionic compounds or covalent compounds that predispose them to dissolve in some particular solvent (the which may not be water). All of these rationalizations are based on an experimental observation. I am sorry if this answer is not precisely what you want. Perhaps you would qualify your question?