Depending on your website's platform it's possible there are no options to have automated publishing from StoryChief to that specific platform.
A popular example is Squarespace, which has no API for publishing articles and is a fully maintained solution where you have no control.
Don't worry though, there are still viable options available to you.
Option 1: William blog
With StoryChief you get a free William blog (on the house). You can use this channel to house your blog articles and connect your main website to this blog by creating links to them.
For example:
https://mywebsite.com would be your main website
https://blog.mywebsite.com would be your blog site.
Your main website would have a link in its navigation that points to the blog. Similarly, your William blog would also link back to your main website.
Learn more about the William blog here.
Option 2: The clipboard channel
The clipboard channel won't automatically publish for you, so you will still be responsible to copy your content to your CMS to get it live. But it does allow you to use all the other features from StoryChief. You can still collaborate on a content piece, publish it to other channels like Medium.com and promote the article to your social media channels.
Learn more about it here.