Within each line of linguistic descent, sound changes are
overwhelmingly regular, such that either all instances of sound x
in a given dialect in a given generation become sound x′ over the
course of the sound change, or, if there are conditions on which
instances of x become x′, they can be stated entirely in terms of
other sounds in the same utterance (i.e., entirely in phonological
terms). (Unfortunately other types of change occur too, and none of
those other types is regular.)
What sort of evidence?
Finally, a question to think about: The definition of linguistic
descent given above is just that, a definition; it doesn’t
say how you can tell that Y is descended from X. Given that
descent is a matter of an unbroken chain of native language acquisition
(not contact), and given what we know about what’s acquired in native
language acquisition, what sort of evidence would you look for if you
wanted to demonstrate that a certain language Y is descended from
another particular language X?