I have no idea what browser I am using (not saavy technically at all) however, I did try to download from the website you stated above. There is a problem with all Mac Airs I believe with regard to playing You Tube video's and getting Adobe !!! If I had known, I wouldn't have got a Mac Air. Now, I just want to fix the problem so I have the option of viewing what I want...it seems you need Adobe flash for most things.
Please let me know...Thank you very much!
The 'browser' is the program you use to connect to the internet and presumably connect to YouTube with? Tell us that and perhaps we can figure out the problem. It's very likely Safari.
Your MacAir is perfectly capable of viewing YouTube, we just need to figure out what's preventing it. To install Flash you need to download the installer from Adobe, then quit Safari, run the Flash installer by double-clicking it and following the instructions. Relaunch Safari and try YouTube.