Amazon API Gateway: how to deploy and stage a newly create API

Went through the trouble of creating a new Amazon API gateway and now you seem unable to find where the invoke URL is defined? If yes keep reading.
Even reading the docs it takes a long time if you are not familiar with the confusing Amazon UI.

Step 1: Click on Resources tab of your API.

Step 2: Next to Resources, click the action button and then Deploy API

Step 3: Define a new deployment stage

Done! Enjoy your invoke URL