Connecting your WordPress blog to your Twitter account, and then sharing blog posts to your feed, is simple.
You can also connect to Facebook and other social media accounts, but lets just focus on Twitter for now.
This is from the WordPress support page:
To enable Publicize, on the Settings→Sharing page click Add new Twitter Connection. You’ll be taken to Twitter where you’ll be asked to approve the connection between your WordPress.com blog and your Twitter account. Click Allow.
New posts will then be automatically shared to your Twitter account, unless you choose to opt out.