AWS API Gateway allows developers to put a uniform API between your services and clients. A servcie could for instance be your custom app or just an AWS Labmda.
The official walkthrough for making Lambda calls from the AWS Gateway works out of the box. It describes how to make a GET and a POST request and map them to self-defined Lambdas.
When I was testing the walkthrough the example was only slightly outdated as follows. When making stages (something akin to Rails environements for the API Gateway), methods must be registered in a sperate effort as follows.
(1) In the dashboard, select your API.