How do we know about the structure of the atom?

Scientists originally thought that atoms were like a 'plum pudding' in that they were a sphere of positive charge with negatively charged electrons scattered about inside it. This was because they observed from experiment that the atom was neutral and also that it contained electrons. Therefore the negatively charged electrons must be cancelled out by a positive charge.

However, a scientist named Rutherford proved this model wrong by firing positively charged particles named alpha particles at some atoms in gold foil. Most of the alpha particles went straight through the foil but some were deflected back the way they had come. 

This lead to our current model of the atom where most of it is empty space, allowing most of the particles to pass straight through. The nucleus is a positively charged collection of protons and neutrons (which have no charge) and so repels the positively charged alpha particles. The electrons surround this nucleus in rings.