Typically, you would pay your collision deductible and the insurance carrier would cover the rest. Once you have established a claim, you can pay the shop directly with a check received from the insurance company or in some cases they can pay the repair shop directly. You can't just get it fixed and then present the insurance co. with a bill though.

Have a couple of estimates done. See how much more than your deductible it will be to fix and then decide whether to pay out of pocket or let the insurance company pay. Keep in mind, even though no other car was involved and the repairs won't likely be that much, they can (and will) still consider that an "accident" and apply a surcharge 6 times out of 10.