The reason for usability testing of websites is to get the site seen through the eyes of someone who is not familiar with it, and to see what they make of it.
I think anyone could do a lot worse than read a great book on the subject. It's Don't Make me Think by Steve Krug.
If you want to dip your toe in the water, you can do usability tests at Five Second Tests and Feedback Roulette.
You can have your site looked at by other visitors and you give back to the community by testing other people's sites.
Doing tests on Five Second Test taught me one big lesson, which is that if I don't know in an instant what the site is about, then those five seconds go by in a flash while I am trying to figure it out.
I just don't 'see' anything else on the page. Well, yes I see a large photo of someone or a big headline - but if I don't know what the site is about then the rest of the page is just an annoyance.
The explanation of what the site is about could be a simple tag line. In fact, a clear sentence at normal size is often clearer than something emblazoned across the site.