I tried out several libraries and after working with libraries like Prototype and MooTools I settled on jQuery. The compelling features of jQuery were the small download size along with the powerful plugin model with a rich collection of available plugins. The other libraries are still useful, but jQuery is what I reach for first and it typically does not let me down.
Web page layout is known as the Box Model. It is a simple concept but working with it can be difficult with many browsers which do not behave in the same way. CSS alone can be intimidating, but if you break it down and keep it simple for a while you can pick it all up gradually. I have found books by Eric Meyer and Jeffrey Zeldman to be the best resources to master the Box Model.