I have a request to create an API to show our Case information on our website (behind a log in page of course) but am unsure where to start. I'm being told I need to create the connection between the two but I've never connected Salesforce to something like this. If someone can point me the direction of a Trailhead I think I can work through it...I'm just not sure where to start. Thanks! A
Sounds like you might be able to get away with the standard APIs - meaning you don't have to build any new APIs; you can use the ones Salesforce already has available for accessing your objects.
Here's the Lightning Platform API Basics module to get you started on what's already available (and there's links included in the units for more resources, but here's one for them). Here's the Design Solutions with Salesforce APIs trail which features that module. It may be a bit overkill for your needs but doesn't hurt to have the link handy.
In the event that you do need something more complex, here's the documentation for creating APIs in Apex.