As I am a beginner to c++, should I be concentrating on understanding how vectors work, or should I just know what they can do when I punch in the text, then worry about the how later, after I can remember the functions as classes?
I can make a vector, get items in it, etc. But I don't understand how it works, should I spend some time into learning this?
I suggest concentrating on using vectors and other standard containers effectively. Use them in the code you write, and learn how to design and implement classes. Once you have such basics down, learn how to do memory management, and possibly also how to use C++ templates. At that point, how to write a simple vector-like container will be obvious.