Bertrand Russell wrote an essay explaining exactly how phenomenalism works from a logical point of view in lecture three of his book Our Knowledge of the External World (1915), which is available in several places on the internet including Wikisource. If that is not detailed enough for you, you might turn to Ernst Mach’s book, An Analysis of Sensations (1897), or Rudolf Carnap’s The Logical Construction of the World (1928) or David Chalmers’ Constructing the World (2012).
But the most famous and readable phenomenalist of them all was Bishop George Berkeley whose Treatise Concerning the Principles of Human Knowledge (1710) lays out a very clear account of phenomenalism with powerful arguments for its appeal.
Ludwig Wittgenstein’s Philosophical Investigations is a classic text ranging over many topics, but sections 398-411 throw doubt upon the existence of sense data. It is a difficult text to work through because you have to read it very carefully and slowly and think through each step, but it is a very rewarding exercise.