This is what the directions say for my new pendant light. Both the (metal) box and the fixture have ground wires. The diagram didn't show how exactly to connect the wire to the ground screw (located on the mounting bracket). Do I wrap part of the ground wire from the box around the screw and then wire nut it to the fixture ground wire? Or does it mean I should connect the fixture & box ground wires and then pigtail to the screw?? Want to do this safely. Any help here is appreciated.
That's an excellent question and it can be quite confusing.
If you're using a plastic box, it won't have a ground screw, just connect the two ground wires together.
If you're using a metal box, there will be a ground screw. In this case, your idea will work just fine.
You could also wire a "pig-tail". That would be the ground wire coming in with the rest of the power supply cable, the ground wire from the fixture, and an extra piece of bare ground wire all held together with a wire nut. Then, the other end of the extra wire goes to the ground screw.
Either way you choose to connect to the ground screw, be sure you wrap the wire around the screw clockwise so that the wire gets pulled into the screw as you tighten the screw. If you wrap it counterclockwise, it will get pushed out from under the screw as it tightens.
I think the intent of the instructions is to emphasize that the bracket needs a proper ground connection, particularly that the mounting screws even on a metal box don't satify the requirement.
If your metal box is fed by NM cable (Romex) or conduit with a ground wire then the box needs to be grounded too. If the ground from the cable is long enough you can loop around the screw in the box then the bracket, then connect to the fixture ground.
If fed by conduit with no ground in the conduit then you could connect from ground screw in the box to the bracket and on the the fixture wire.
You could certainly pigtail all the connections if the wire is too short.