I'm from Columbus (Franklin County), Ohio.
I took my class over the course of a weekend, the following week I was busy w/school and work, so I had to wait until Friday to turn in my paperwork.
I went in on a Friday afternoon with my $45, passport photo and certificate of completion (for the Ohio CHL class requirements)...
They called me the following Monday when they opened and told me to come pick up my license.
Total time between applying and recieving a license: about 42 hours.
Edited to add: It can take up to 45 days according to everything I've read. IIRC a friend of mine from the same class had to wait about 30 days for his, but I've never been arrested. He'd been arrested for a misdemeanor something-or-other, so there are pobably other factors that can delay getting your license.