This is most obviously the case with vocabulary differences. There surely are American English speakers (say, about 10 years old) who know the words ass or truck just fine, but have never heard the words arse or lorry and would find them completely opaque without context. Learning that these words exist as equivalents to the former two used in British English is essentially L2 acquisition, and does not really fundamentally differ from learning that e.g. their Dutch equivalents are kont and vrachtwagen. Nothing here could be predicted just from knowing American English.
Grammatical differences can work the same as well; they can be learned as foreign patterns that you understand but do not employ in your own language use. Phonology is slightly more interesting, in that it can be learned by means of a kind of naive comparative method. If you find someone saying [də], [dɛn], [diːz], [tʰoʊ], [bɜɹt], [wɪt] for the, then, these, though, birth, with … this naturally sets up an expectation to always hear [t d] for /θ ð/, and you might be also able to guess what [maʊt] or [bɔdɚ] are supposed to mean. Much conditional sound change can be also parsed by this means, though as far as I can tell generally not properly learned by linguistically uneducated speakers. (”Sometimes they have X rather than Y” but usually no knowledge of conditioning factors.) But, again, this still requires some base exposure over time and cannot be predicted in advance.