To find out if someone has been arrested, you can check the arrest log of your local police station online where information pertaining to arrests is updated within the last 24-48 hours. You could also contact their booking Office through the telephone.
1 Additional Answer
The National Victim and notification network provides a free online service called VINELink for people to check booking information around the clock. Provided you know the state where one got arrested, you will be able to access it on VINELink.