Insurance companies and laws vary from state to state but generally getting charged with being a Minor in Possession (MIP) will affect your car insurance rates. Drivers under the age of 25 are found to be inexperience so typically have higher rates already, so getting charged with a MIP will make the risk for the insurance company to cover the youth even higher and thus raising their auto insurance rates even more.
Minor in Possession is what a person under the age of 21 in possession, ownership or control of an alcoholic beverage can be cited with by a law enforcement officer. The punishment for this citation varies from state to state but most offenders are fined and possibly given community service. Harsher penalties in certain states include revoking the driving privilege of the cited individual for a period of up to one year.
If you are found guilty of this violation in some states once you turn 21, and have not been cited for anymore alcohol related incidents, you may apply to the courts to have the conviction expunged. This may or may not help your insurance rates after that time.
Auto Insurance for Young Drivers is an article you might find of interest.