Almost every town will probably have a summer softball league through their parks and rec department, if not there's probably some sort of organization that runs it. In Lincoln, it's run through the P&R Dept. In Omaha, it's run privately.
My teams started as church teams and sorta morphed from there. Especially the volleyball team. Softball teams are still sponsored by the church. So, maybe if you have a group of friends that wants to play that might be a good place to start, otherwise, the leagues might have a sub list, there's always a team that needs a sub and you can try it out from there. Sometimes you might find a team that really fits you and them. We found one of our best vball players like that, she played for us for two years before she went and got married.