The penalty for being convicted of driving without insurance in Nebraska is an automatic suspension of your driver's license.According to the Nebraska DMV you can get your license reinstated by paying a $50 fee and filing proof of financial responsibility. This is done in the form of an SR-22 Certificate.
You will need to keep this type of insurance on file for 3 years. Failure to comply will result in the suspension of your motor vehicle operating privileges. Follow this link for a quote on SR-22 insurance for Nebraska.
Since you were involved in an accident when you did not have insurance there is more to your suspension. To get your license reinstated you will have to prove that you have made restitution for any damages you inflicted on the other party. For more details, check with your local DMV or look on their site for accident suspensions.