How do I get points off of my driver's license for insurance purposes in Ohio?

Depends on your States policy. Most States it is 3 to 5 years before the points are dropped from your Drivers License. If you want low insurance rates you are going to have to learn very quickly to keep your foot out of it.

Yes. Allow 36 months to pass, and insurance will no longer consider it assuming you don't get any more tickets in the interim. If it's your first ticket, you might ask the judge about paying the fine and going to classes to keep it off your record. The fine will cost, the school will cost, but if you complete the school, take your certificate of completion back to the court, and go the time, typically 6 months without another ticket, it will not go on your record and the insurance will never know.