Similar to publishing a Guide, first you must make your Space public in order to publish it to your website.
The easiest way to publish a Space is to create a new Space and for permissions select "Public - anyone on the internet":
To make an existing Space public:
1. click on the Space
2. click on "settings" in the top right
3. click on "Space Access"
4. Select "Public - anyone on the internet can access this channel", and confirm with selecting "Save"
NOTE: You won't be able to make an existing Space public until all guides within the channel are also public.