How can I share the Cooking StackExchange site on Facebook (I can't find the social share facebook button)? I've looked for the button on
http://cooking.stackexchange.com but could not find it.
There is no sharing button for the whole site. Instead, each post has its own sharing button. It is hidden in the "share" link below each post, on the left side. This question from our parent meta explains it with pictures.: How do I "share" a link for the new badges?.
You can also share the whole site manually. You have to select the URL of our site, http://cooking.stackexchange.com, and copy it. Then open Facebook, and in the box which allows you to make a new post, paste the URL. From there on, it will work the same way as if you had clicked the button. In fact, this is everything the Facebook button does for you - it opens the Facebook page, starts a new post, and pastes the address inside. No magic, you can do it yourself. By the way, this works with any site on the Internet, not only with ours.
If you have an adblocker enabled, you won't see the buttons. They are removed for privacy reasons, as they track user behavior. You'll have to go the manual route then.
This is what it looks like when you manually share your own question above: