How is static electricity created? What are the charged particles associated with static electricity?

Static electricity is all about electrical potential energy stored in objects. My approach here will be classical, and include Coulomb forces. A more modern approach would use Quantum Mechanics.

To create static electricity, all you need to do is to pick up some charged particles (say electrons) and put them in an almost static configuration, that is, one in which they are not accelerating.

Now, as they are charged particles, they will interact with themselves. This interaction comes from the Coulomb forces between them (classical point of view).  But if we put our charged particles in a statical configuration such that accelerations are not allowed, there will be no net forces present, right? Yes, because to maintain our particles with no acceleration, we needed something to fix them in space, that is, an opposing force! So, suppose they are separated by "walls".

Now we speak of fields! All particles have electrical fields which are basically a way to associate to each point in space around the particle a value E and a direction. This E, when applied to another charged particles, gives rise to the Coulomb force.

This field follows some rules, like the superposition principle. This means that if you have a bunch of charged particles like we do, you can sum the electrical fields in a natural way. So our system has an electrical field of its own.

Associated with the electrical field, there is a potential field. Much like the electrical field, this associates a value V to each point in space (without direction, although we can still obtain this value by doing some math operations). The electrical potential energy is the energy required to bring a particle from a potential field A to potential field B, that is, the difference between these fields. To calculate the energy of our system, we calculate this energy as if we bring each particle from really far distances, where the potential field is practically null, to its position in our system.

Now, this electrical potential energy associated with our particles is the static electricity! If we remove our walls, then this electrical potential energy will be released and the particles will move following its rules.

In real life, the charged particles are electrons and "holes" (atoms with fewer electrons than normal). To create statical electricity, all you need to do is to remove or add electrons to an insulated object - the space that separates the object from any conducting surface represent the walls holding the electrons. You can do this to your hair, by combing it! And one way to release the energy is to touch a metal car door (the electrons will fly from your hand to the metal) - but keep in mind, this is uncomfortable!