The amount of an auto insurance increase in premiums after your first accident will depend on a variety of factors such as state law and your insurance company rating plan so it is difficult to give an actual average amount.
Besides these first 2 factors, a rise in rates can also depend on the nature and severity of your vehicular accident and who is found to be at fault. A minor accident may be forgiven under state law or by an insurance company, especially if you are not found to be at fault. Some companies have a "forgive the first accident" policy but the qualifications for this and if this is available differ from insurance company to insurance company.
If you have had a good record, and you have been with a particular company for more than five years, there are some car insurance companies that will not increase your rates if you are found to be at-fault in a relatively minor vehicular accident.
If instead you were driving drunk or were racing on the street and have an accident, you are likely going to be getting a big rise in your insurance premiums. There could be severe insurance and legal consequences if there is a major accident with serious bodily injury and you are the at-fault driver. There could be a dramatic increase in insurance rates or even a cancellation of coverage, subject to state law.
To find out how much your insurance could go up after being involved in your first accident contact your current insurance provider for an explanation of their rating system. Also insurance companies must file their rates with the state's insurance regulator if you instead would like to contact them for information on your provider's rating system.