All you need is an easily obtainable and free Windows Phone developer account. If you installed WP8.1 you already have one. You need to download the associated SDK

For the actual YouTube app go to this link https://mega.co.nz/#!0YcGiSrC!rb_… and download the app and package.

Unlock your phone with your developer account and use the SDK to sideload YouTube. Certain phone models - non-Lumias in the main - need to sideload using the alternative app that is included with the YouTube download.

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This process looks more complicated than it is and is worth the effort. The Microsoft YouTube app is a model of user-friendliness and eye-candy. It's really a definitive WP app. It's super intuitive, has every YouTube feature in an extremely fluent and navigable interface. Plus no ads.

Profit (as they say)

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