It's super quick and easy. Ready? Let's go!
The first step is, of course, setting up your Twitch account. Once you are done with that, go to https://belive.tv/twitch or https://belive.tv/.
Following the first link will bring you to this page:

Right in the middle of it, there's a beautiful "Sign up with Twitch" button. Click it! You will be prompted to a window that asks you to authorize BeLive's access to your Twitch account.
Following the second link will bring you to the BeLive main page:

Click on "Sign up with Twitch", and you will see the same authorize window as in the first case:

Click "Authorize" button :) Aaand that's it! It will open your personal BeLive account on Twitch channel, something similar to:

You are all set and have your BeLive connected to Twitch :)
P. S. In case it logs you into your Facebook account instead of the Twitch one, please try logging out on belive.tv and then follow all the steps from the article.