Electrical – How to figure out where power is coming from in 4-way switch wiring

One of B1 or B2 carries live to the light fixture, and the other carries it to another fixture somewhere else. W3 carries live to the switch, and B3 carries switched live back to the light fixture. B3 is capped off temporarily because it could carry live, depending on the switch position.

To install your light fixture, you'll need to connect the light's live wire to B3, its neutral to W1 + W2 and ground to the other grounds. While you're working in there, wrap a piece of black electrical tape around the insulation at the end of W3 to indicate that it's carrying live, and do the same at the switch end too.

This is a circuit diagram, adapted from one I drew for a similar question:

I didn't show the ground wires because they would have made the diagram more cluttered and as long as they're all connected together, you're OK.

What you have is power to the ceiling, and 3-Way switches.

My best guess, is to wire the two blacks together in the ceiling, with a wire nut. One of the whites should be marked. This will go to the Black of the fixture. The other white wire should go to the white of the fixture. And then connect the ground.

So the path will be Panel Hot -> Black wire -> [ Switch Common -> Switch Travellers ->Switch common -> ] WHITE -> Light -> Panel Neutral.

the stuff in Brackets [] is in the wall, and you won't see it.

See this http://diy.blogoverflow.com/2012/01/poles-and-throws/ for more information on 3-way switches.