Static Electricity needs to be explained based on atomic particles. We know that atom is made of protrons, neutrons and electrons. Neutrons have no charges, so we don't talk about them here. Protrons are in the center of the atom, so they are not the ones that cause static electricity. Electrons are the ones that surrounds the protons, and they can move freely, so they are the cause of static electricity.
Conductors conduct electrity so well, it is unlikely for them to have static electricity since they can't build up charge differences. But insulator can build up charge differences. When two pieces of insulator made of different materials are rubbed togetther. electrons may move from this material to the other material, and eventually it builds up a charge difference and that's static electricity.
For static electricity, opposite charges will atttract each other, while the same charges will repel each other.