Where I work, the NOTAMs are prioritized automatically by a computer system and then checked manually before briefing docs are printed. Then, when preparing the briefing it's up to me (the flight ops/dispatcher) to go through and additionally highlight the really relevant (or new) stuff.
I've briefed crew on NOTAMs in a few seconds flat.
But then again, they have to have something to do during that long boring cruise: Test each other on the irrelevant NOTAMs!
