Most major cities, and even smaller towns, now have nightclubs that cater to the lesbian community. Some gay clubs will have a girls night that is designed for single women to meet other single women. You can find listings for clubs and bars near you online. There are plenty of websites devoted to listing the lesbian friendly bars in your area.
If the bar or club scene isn't your thing, look for bookstores that stock gay and lesbian books. Many reading groups meet at larger bookstores. You can find other single lesbians at some of these reading groups. Look for groups that are focused on women's studies or books by noted lesbians or lesbian supporters. If you're fortunate enough to live in an area that has a specialty bookstore, then this will make it much easier.
Pride events are a great place to meet other lesbians in a safe environment. Since most pride events are staffed with plenty of security, you can be yourself without any concerns. Pride events also tend to have a lot of activities, both for singles and couples. A simple online search will allow you to find the closest pride event to your community.