>What are and how do I use vectors ?
Vectors and arrays are conceptually analogous. Due to operator overloading, you can use a vector in much the same way you use an array, with the added convenience of built-in functionality like automatic growth and useful information rolled up into a single object.
>I have read some tutorials on them but I don't understand fully how they work.
I could give you an implementation of the class, but I don't think that would help much. Perhaps if you show us exactly what you do and don't understand, we can fill in the blanks.