To create API key follow the below steps:
1) Go to the Google Developers Console and Select a project.(https://console.developers.google.com/project)
2) 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.
3) In the sidebar on the left, select Credentials.
4) The API supports two types of credentials. Here, click “Create New Key” button and it opens one dialog box. In this select “Browser Key”.
5) It opens new window. Here, no need to enter any data. Click create button. It displays “API key”.
6) Copy this key and enter in “YouTube API key” in the below path.
Go to WP admin -> Video Gallery -> Settings -> search Enter YouTube API key under user video setting.