There are lots of free software programs (either as standalone programs or as browser extensions) that can do the job. However many of them will only work with specific websites (such as Youtube or Dailymotion), rather than across a wide range of sites. The best way to ensure that you can capture video from almost any website is to proceed as follows:
1. Use either Firefox or Internet Explorer as your web browser for capturing video (and not, for example, Chrome or Opera).
2. Install the Ant Video Downloader:
https://www.ant.com/video-downloader/
3. You'll then see a new icon at the top-right corner of your browser window, with a little downward-pointing arrowhead next to it. Click on that arrowhead to enter Ant's settings and choose where you'd like your videos to be saved to. (There are further options available there but you'll probably find the default settings are OK anyway).
4. Go to a video website. You'll see that the new icon starts 'rolling'. Simply click on it to save the video file to your your designated location.
Job done!