In order to install an application that is not on available on Google Play, you must first configure your device to download third-party applications.
Go to Settings > Security. Then, go to Device Management, and check the box next to Unknown sources.
Download and Install TubeMate
Download TubeMate to your Android tablet or phone.
Once the file is downloaded, open the notifications panel. Alternatively, you can go to Settings > Storage > Downloads.
Next, click the tubemate_1-5.apk file. Tap Install to begin the TubeMate installation.
Once installed, click Open to run the application.
Download Videos from YouTube
The TubeMate interface is similar to YouTube, but it allows you to download videos. To do this, click the magnifying glass located in the top right corner, and find the video that you'd like to download.
Play the video. To download it, click the green arrow located at the bottom right of the playback window. In the window that opens, click Download. Choose the video format, and then wait for the download to complete.
View Your Downloaded YouTube Videos
To view your downloaded videos, go to Settings > Storage > Photos /Videos.