There are dozens of websites that let you upload and watch videos online for free, provided you don't mind watching a quick advertisement. Here's an online tool that will let you download those videos directly to your computer, and without the advertisements.
Visit savefrom.net in your web browser and you'll see a list of all the video sites they support, including all the popular ones like YouTube, Vimeo, DailyMotion, Facebook and several others.
Let's say you wanted to download a video from YouTube. Just open another tab in your web browser, and go to the video page on YouTube.
Click "Share", and then copy the video link.
Paste that video link into savefrom.net and press enter to download the video.
You'll find the video in your downloads folder, and you can also choose the level of quality for the video. The 720p option will provide the best quality, but also will have the largest file size, so choose a smaller video format if you want a smaller file size.