How to make calls to youtube Api with user Api key

I discovered that the youtube API has a limit of resource that can be consumed by one API key.

This is called quota and its not related to the API key but rather related to the project. You have a quota limiting the number of requests that your project can make against the API. see quota calculator

This will be a multi user app, So i'll like to build out the functionality in which when a user signs into the app via gmail, the user's API will automatically be used to consume resources from the youtube API , without the user having to go digging into the Youtube API documentation to get there API key.

If you want to allow a user to login to their YouTube api account then you will be using Oauth2 client credentials and not an API key. The API key will only allow you to access public data no private data will be available.

Any ideas of how to automatically enable a new user’s api key to make the call , instead of my api key ?

API keys are not user specific you cant create a new user api key. Thats not how API keys work, api keys enable your application to access public data on YouTube it is defined by you manually though the Google developer console and identifies your application to Google.