[upthesaukee]

is also know as OTC coverage, Other Than Collision. Collision coverage would be your vehicle colliding with another vehicle or object (such as a tree, rock, wall, bridge, etc). If you do have collision coverage, you can put a claim in for your damage through your insurance company, and they will subrogate (go after) the other guy's insurance company to recover the money. If there is a question as to comparative negligence (you are partly to blame), your company may withhold your deductible until they get reimbursement.
If you do not have collision, you may go directly after the other insurance company.
In either case, you most likely will not be charged any points on your license. However, too many not at fault accidents, and your company may take a really close look at continuing coverage for you (whole different thread, not appropriate for this forum).