Blog commenting would be the first and easiest route. Takes time, but it can and does get your content more social shares. And blog commenting can lead to other things such as guest posts, networking and new connections.
Though your content needs to be good and compelling, worth getting shared in the first place. Sure you know that.
And the obvious, build your social following in the first place. Too many people seem to think it can or will build on it's own, just not the case. Usually not. Sure takes some work.
Also make sure you push visitors to follow you social accounts themselves. Profile links. So many people only put up share buttons for content.