Hi. I am, I think, an intermediate-level computer user at best, and I thought I would briefly describe the way I was able to download some videos from YouTube...in case this helps others who are in a similar situation. I have both Internet Explorer and Chrome...and they both hate me

so I used Real Player, since JimN said Real Player would work.
Open the Real Player program.
Click on the Real Player logo in the upper left corner.
Click on FILE, then NEW, then NEW WEB BROWSER.
If you know the web address of the video you want (maybe it's open in another window on your computer), then copy-and-paste the web address into the Real Player address bar.
If you don't know the video's URL, then type in the web address for YouTube. The YouTube website should come up on your screen, and now search-and-find the video you want.
To play the video, you should get a red PLAY arrow/button. Click that, and the video will play. Keep an eye on your screen, and you should see a small pop-up above the video that says REAL PLAYER DOWNLOAD THIS VIDEO NOW...and when you see this, click on it. It will immediately start downloading the video into your Real Player Library.
I never knew it was possible to download videos from YouTube, so I am quite happy to have learned how to do this. Thanks to everyone who wrote instructions on how to do it.
Kind regards,
Donna