The basic approach isn't super hard to understand, though the details are tricky. The resolvers partition the keyspace; a write ordering is imposed on transactions and then the conflict ranges of each transaction are divided among the resolvers; each resolver returns whether each transaction conflicts and transactions are aborted if there are any conflicts.

(In general the resolution is sound, but not exact - it is possible for a transaction C to be aborted because it conflicts with another transaction B, but transaction B is also aborted because it conflicts with A (on another resolver), so C "could have" been committed. When Alec Grieser was an intern at FoundationDB he did some simulations showing that in horrible worst cases this inaccuracy could significantly hurt performance. But in practice I don't think there have been a lot of complaints about it.)