This generally depends on your community. Often promoting a bookgroup takes care of itself, but you still need to get the word out there that there is a book group happening at the library. Simple promotional material in the library, a mailout, utilising your local bookshops to advertise as well. There are many ways we can promote our book groups to our community.
Perhaps the most effective first step though is to tell your staff about it. Front line Circulation staff are the ones having converstaions with all manner of people and are the best source of promotion through word of mouth.
Should budgets allow a simple advertisement in your local paper will also work wonders, not to mention local radio stations.