Every library does story time differently. For some, it is a "come one, come all" thing where you just show up and get some stories read. My library requires you sign up ahead of time, but they do really neat things for the children with fun crafts, handouts, and treats.
And not all storytimes are at the library. We have a non-profit center close to our home that focuses on the history of the American West. They do a free storytime weekly that is full of stories, games, crafts, and food, and it is come one, come all, no sign ups required. Learn about the resources you have around you by asking moms with older children, reading the papers, and checking websites.
Storytime offers a love of reading along with a social outing that is low-pressure. This is a great winter, rainy day, or hot day activity!