Looks like you've got a 1 gang 5 hole outdoor electrical box, like this.

A couple weatherproof lampholders,

and a motion sensor.

You should be able to find each of these sold separately, at your local hardware or big box store. To replace them, you'll have to be comfortable doing electrical work, and working from a ladder. If you're not comfortable with either, contact a local Electrician to complete the repair.

Replace the broken bits

If you have no problems with this type of work, the repair is quite simple. Start by turning off the power to this circuit at the breaker, and verifying the power is off using a non-contact voltage tester. Next remove the cover from the box, which is likely held on by two screws. This will reveal the wiring inside. Take a moment to note (and jot down) how everything is connected. Taking pictures is often helpful.

Remove the lampholder

Locate the wires going to the broken lampholder, and follow them to where they connect to the other wires. Disconnect the wires from the broken lampholder from the other wiring (likely done by removing twist-on wire connectors), making sure to remember where they were connected.

There may be a locknut where the lampholder threads into the box.

Loosen the locknut with a pair of tongue and groove pliers (channellocks), then simply unscrew the lampholder from the box.

Finishing up

Installation is the opposite of removal.

Follow the same procedure to replace the motion sensor.

Before replacing the box cover, inspect the gasket and replace it if necessary.

Strictly speaking, that round metal mounting bracket on the back of the fixture is supposed to be secured to an electrical box.

It can be a shallow box, but it's supposed to be a box. You must protect the wires. You want that new garage to still be there 10 years from now.

I can't really tell from the photo, but the right shallow metal box should fit within that recess on the back of the fixture without you needing to cut a hole in the siding. But if you have to cut a hole, then you have to cut a hole (if you do, rent, borrow or buy a holesaw for your drill big enough for the box).

You could attach the box through to the OSB with screws, although personally, I'd lay a 2x4 flat side against the OSB inside the garage, toenail it into the studs on both sides, and screw the box directly through the OSB into that 2x4. So a stiff breeze or errant basketball doesn't knock your light fixture off the wall. :-)

Drill a hole through the OSB and the 2x4 big enough to feed the cable and to accommodate the clamp that holds the cable in the box. The cable has to be clamped into the box.

Then attach the round mounting bracket that came with the fixture to that box, wire everything up, attach the light fixture to the bracket that you attached to the box. That's the way it's designed.

If it's a metal box, it has to be grounded (screwing the grounded mounting bracket to it will accomplish this).

You also have to secure the cable inside the garage as dictated by your local electrical code.

Finally, I'd use a dose of waterproof silicone or caulk around the box, and then again around the fixture itself after it's mounted, to make sure water doesn't seep inside.

Good luck!