The quick answer is with the Circuit Clerk's office. There are typically two court clerks in Arkansas Courthouses. The Circuit Clerk and the Probate Clerk. The Circuit Clerk is the correct court clerk to use when your are filing for divorce.
If you are using grounds other than separation, you just have to be separated. This means that the couple must live separately, without cohabitation (living together). So if you are using other grounds for divorce you can be separated for one day.