On most days, Yahoo processes waiver claims between 4-6 AM Eastern time.
I'm not sure exactly when you can get them plugged into your lineup.
Last, you can't tell if anyone has put in a waiver claim. Unless you're the commissioner, I believe. But even if you are, don't cheat. In a league last year my commish took a player off of waivers early to put him on his team. When the other players questioned why he had done it, he said it was because no one had a waiver claim on him. So, don't be a dumb commish.
Ron Paul 2008