2 wire light fixture with black and green wires

The power (from the breaker) is likely at the light fixture. When you hook black to black and white to white, the light is powered directly from the breaker. In this configuration, when you flip the switch on you create a short through the switch.

What you need to do is hook it up like this.

Notice the white wire that runs between the switch and the light has a black stripe on it (in above image), that lets anybody that works on this light in the future know that the wire is switched. You can mark the wire using a bit of electrical tape, or a marker.

Figuring out which wires come from the breaker, and which go to the switch will require some tools. First Turn off the breaker, and verify the power is off using a non-contact voltage tester. Now pick one set of wires to work with first (one black and one white from the same cable). Turn the switch to the on position, and use a multimeter to check continuity between the two wires. If the wires are connected (low resistance), these are the switched wires. If not (infinite resistance), check the other set of wires. If neither pair pass the test, contact an electrician.

If at any time you don't feel comfortable doing this work, or you don't have the proper tools to complete the task. Contact a local licensed electrician.

The instructions for the fixture are only correct for a metal box. If a metal box was used, the box itself would (should) be grounded. The bracket that holds the light would then be connected to the box, which would make the bracket grounded. Finally the ground wire from the fixture would attach to the bracket, grounding the fixture.

In the case of a plastic box, the box is not grounded. All ground connections must be made by connecting the ground wires together. So in your situation you are correct, you'll connect the ground from the supply to the ground from the fixture using a twist-on connector (or other approved connection).