1. Open this website www.savefrom.net in a separate tab of your browser
2. Now Open the website where the videos are located like www.youtube.com and play the video. Right click the video you want to save and click COPY VIDEO URL, now go to www.savefrom.net web address you opened before and paste on the download search box and click download. This will search for the different easy downloadable formats for you to save to your PC. If you want to keep playing it on your phone, I will recommend either you click any of the MP4 or 3GP and it will automatically be downloaded to your PC or phone.
3. There are other 3rd party softwares that can grab videos from youtube or other video sites immediately the video is being played like ORBIT DOWNLOADER, YOUTUBE DOWNLOADER etc. If you need any of those softwares, kindly click the name above to link you to the free download page.
Feel free to comment and ask your questions.