Automatically fill custom field value on post publish/update

I’ve searched around a bit, and I’m having trouble finding an answer to this question. What I’m trying to do is automatically fill a custom field when a post (custom post type) is updated or published. Ideally the completed script will call out to an API and fill the custom field with the resulting information whenever a post is created or updated. For right now though, I’m just trying to automatically fill my custom field with a simple string for testing. Here’s my code: