Consuming a CAP Service from Custom UI5 App

I am currently trying to build a full-sized application based on the SAP Cloud Application Programming Model (CAP). I followed the documentation and exposed a working service locally. After that, I implemented a custom Fiori App in the /app Folder.

Now I want to consume the CAP Service in my Fiori App, but I am not able to link the two. In the documentation, they are just focusing on Fiori Elemtents which does not really help.

Thank you for your answers, I really appreciate it!