There are two ways you can do this.
If you don't have a Twitter account linked to Sharesome, you can find the "Share on Twitter" button on any post, once you hit the Share button. This will open up a new page, asking you to "Log in and Tweet". It will require you to add in your Twitter credentials in order for the post to go through.
If you have a Twitter account linked, besides the previous way, you can also find a checkbox in your Posting Menu. If this is checked, the post you create on Sharesome will automatically get posted to your Twitter profile as well.