The general term for what you're describing is onboarding. There's all sorts of different approaches but the highest value - quickest thing to do is just sit down with a developer who might want to use your product and watch them try to sign up and use it.

I entered my email in your site and it says: "Thanks! We'll be in touch soon."

This is also really confusing given the "Get started in 29 seconds" thing - which almost seems like I should cut and paste into a commandline? But it doesn't have any directions? Is there an API key?

Hope that helps.