Here are links on how to cross-post into other channels like Twitter and Tumblr.
As far as sharing to other social media destinations, you’ll pretty much have to share a link to your post on your social media feed/timeline.
You can add some JavaScript that will give you a Share button/link at the bottom of your post to help make it easier to share. Here’s an example of adding a Facebook Share button.
As far as site aggregators, I have no idea. Normally, other people add a link to your post in there so they can talk about it. I’ve seen some other bloggers share a link to their own post to increase traffic, but I don’t know if that’s the proper way to do it.