Transaction processing in PostgreSQL uses multi-version concurrency control (MVCC) to allow concurrent transactions to read and write tables without blocking each other. MVCC works by storing multiple versions of rows and filtering out rows that should not be visible based on transaction snapshots. Table-level locks are still used to prevent entire tables from being altered during transactions. The system guarantees atomic, consistent, isolated, and durable (ACID) transactions using techniques like tuple visibility information and locking.