You file a claim by calling your State Farm agent and telling them what happened. But before you do that, you need to know two things. The first thing is ignore the answer from Frank completely.
The second thing is that the damage you have is the result of a hit & run, and hit & run damage is only covered by Collision coverage. If you don't have Collision coverage, your policy won't cover this damage. If you do have Collision coverage, your policy still probably won't cover this damage. Collision coverage almost always comes with a deductible, and the deductible is the part of a loss that your policy does not cover. Collision deductibles are usually anywhere from $500 to $1000, and most side mirrors (parts and labour combined) are worth way less than that.
Go to the nearest repair shop that you trust, and ask them for an estimate. If their estimate is less than your deductible, you've got no reason to file a claim with your insurer. If it's more, definitely file a claim by calling them up and telling them you need to file a claim.
NOTE: Since State Farm only operates in the US and Canada, you definitely won't risk having your rates increased by reporting this to them. Only at-fault claims can affect your rates, and being the victim of a hit & run is totally not an at-fault claim.