Vectors, dot products, cross products etc

I really need to understand this, all of this. Whenever I find an article it's usually full of mathematical lingo which just confuses me more.

Basically, has anyone got a link to an article on this (and everything / anything related) for the simple-math-minded person?

Or a nice description.

EDIT: Oh I'm reading this right now and understanding most of it: http://www.geocities.com/siliconvalley/2151/math2d.html (the sectons on vectors and such)

EDIT2: And I think another barrier is that I don't understand where we'd use these in practice - what would we use them to solve?