To allow visitors of your blog to share your posts, you can enable the AddThis Social Share plugin.

The AddThis Social Share plugin makes it quick and easy for your visitors to share your posts via Twitter, Facebook, Tumblr, Email, and more.

Both the Jetpack Plugin's Sharing widget and the AddThis Social Plugin allow for social share options. If you activate both, published posts will include a lot of repetitive buttons. However, you can turn on Sharing and turn off AddThis on individual pages or posts.

See AddThis Social Share Plugin guide for instructions on adding the plugin to your site and removing it from individual pages / posts.