Going to organized walks (I am a member of a local branch of the botanical society), trying to identify with the key myself, reading articles about different species when they exist. Not usually the whole family at a time. Rather various taxons that appear in the area relevant to me. And then some interesting ones that I never saw myself from the literature.
However, some genuses are simply difficult and require a specialist. One way s to try ID yourself, but collect the specimen and submit to the herbarium where you know the specialist comes from time to time or even works there. Or submit to iNaturalist if a specialist is active here, but that is not true for some taxons I am interested in.