You can use HybridAuth to connect to Google API and Register your Application / Projet in Google ( HybridAuth already enables Connection to Google , see Documentation for reference ) and When you register your projet with Google , you can start to add / Enable the right Google API by browsing API List Items available. You will find an API Called YouTube Data API v3 , Click on it and Enable to Change Status to ON.
Once done , then your registered projet with Google enables YouTube API , and you have to go to Credentials to generate your keys.
Hopes it helps ...
Here is a usefull link for you to get Started with YouTube through Google :
Source : https://developers.google.com/youtube/registering_an_application
Title : Register your Application with YouTube via Google
Go to the Google Developers Console.
Select a project.
In the sidebar on the left, select APIs & auth. In the list of APIs, make sure the status is ON for the YouTube Data API v3.
In the sidebar on the left, select Credentials.
The API supports two types of credentials. Create whichever credentials are appropriate for your project:
OAuth 2.0: Your application must send an OAuth 2.0 token with any request that accesses private user data. Your application sends a client ID and, possibly, a client secret to obtain a token. You can generate OAuth 2.0 credentials for web applications, service accounts, or installed applications.
Learn more
API keys: A request that does not provide an OAuth 2.0 token must send an API key. The key identifies your project and provides API access, quota, and reports.
If the key type you need does not already exist, create an API key by selecting Create New Key and then selecting the appropriate key type. Then enter the additional data required for that key type.