To connect your Twitter account, simply add a channel and select the Twitter option:
Then, make sure your account is enabled to receive direct messages from anyone. You can do so from your Twitter Security Settings.
Note that Twitter currently limits accounts to 1,000 direct messages sent per day. If you expect to exceed this number, you'll need to contact Twitter directly to request that they lift that restriction for your account.
Authorize the integration, then you're ready to send direct messages:
Your twitter handle will appear on your account page as a channel: