There are two types of accelerators: linear and circular. In the linear accelerators the particles are usually made to collide with a fixed target. In the circular accelerators they usually collide with each other.
A particle is accelerated by letting it pass through electrical fields that have a potential of several billions Volt. A circular accelerator uses electromagnets to force the charged particles to go in curved trajectories.
Different kinds of particles can be accelerated, e.g. electrons, positrons, protons and different kinds of ions. The only requirement is that they must be stable and charged.
To start accelerating particles in the CERN accelerator system a metal wire is heated until electrons are liberated. Some of these are fed through linear accelerators to the smallest circular accelerator. Other are made to collide with a metal target whereby creating positrons that are guided the same way as the electrons. The electrons and positrons are accelerated in different accelerators until they are inserted into LEP (Large Electron Positron collider) where they are made to collide with each other. They collide in one of the four detectors that analyse the particles that were created in the collision.
LEP has now been shut down to give room for a larger accelerator, LHC (Large Hadron Collider), which will collide protons at a much higher energy.