"Well read" is a somewhat old-fashioned term that has the connotation not just of what one's read but what one has learned from reading. You can be well read on one subject (e.g., he was well read on the poets of his day) or even in one book (he was well read on the Bible and the Apocrypha). But the connotation is that the person knows these things now. Even if you read all of 20th century modernist literature, you're not well read on the subject unless you've retained some knowledge of it and gained some perspective.
A person who is generally well read has read sufficiently around all subjects that a well-educated, erudite person should know about, i.e., science, politics, history, literature, poetry, philosophy.
I would say that I'm well read in literature, poetry, and philosophy, with a passing knowledge of some other things. Victor Davis Hanson is, no doubt, well read on the ancient world, politics, geography, history, Latin, Greek, etc., but not necessarily on modern art and literature.
This is the precise idiomatic meaning of well read. If you want to just take the literal terms for what they mean superficially, then you could say it means a person who has read something well, which is not the meaning at all.