There are many JavaScript frameworks out there, but one of the most popular is jQuery (which I'm sure you may have heard of). As well as being a great DOM manipulator, it also has a UI library that has a ton of features like accordions, tabbed interfaces and progress bars etc which are super easy to get going with.
http://jqueryui.com/
On the other hand, if you're after pretty heavy app development, I hear good things about ExtJS:
http://www.sencha.com/products/extjs/
There won't be a silver bullet to developing with JS and HTML5, so it's best to find what will suit your specific needs. Ignore the hype and go with what is right for you.
If you're after something more template driven, then I hear Angular JS is great:
http://angularjs.org/
But, this is more for your JS apps rather than 'websites', as it is totally dependent on JS and can't work without it (no graceful degradation).
There are tons of frameworks out there, and many come and go. It's best to do some Googling!
Good luck.