How did Scientists figure out how many electrons and atoms are in a given element

http://en.wikipedia.org/wiki/Atom#Origin_of_scientific_theory
That site will explain the gist of it. The smallest mass of an element is an atom, which has electrons and neutrons inside it. People spend years studying this so the website above should at least satisfy your curiosity.

i assume you mean how many protons, neutrons and electrons are in a given element.
For an answer i dont remember exactly but it was based on many different experiments. http://en.wikipedia.org/wiki/Oil_drop_experiment then early mass spec