The most direct methods of observation of particles are those which make the particle leave a visible track.  These include:

• The cloud chamber.
  When an energetic charged particle passes through matter, it knocks electrons out of the atoms in its path, leaving a trail of positive ions behind.  In air which is supersaturated with water vapor, the ions trigger condensation of the vapor. The track of the particle becomes visible as a trail of water droplets.
  
   
• The bubble chamber.
  In the bubble chamber the supersaturated water vapor of the cloud chamber is replaced by a superheated liquid.  Ions created along the track of a charged particle provide nuclei around which boiling occurs, and the track becomes visible as a trail of bubbles.  The bubble chamber has now superseded the cloud chamber for most purposes.
  
   
• The spark chamber.
  An electric discharges passes more easily through a gas which contains ions.  If a charged particle passes through the region between two plates, with a voltage applied across the plates, a discharge will pass along the trail of ions left behind by the particle, thus making its track visible.  The gap between the plates must be fairly small, so spark chambers are usually used in large arrays.
  
• Photographic emulsion.
  A charged particle interacts with the silver bromide in the emulsion.  The record of its passage through a photographic emulsion constitutes a photographic image.  Photographic emulsion has been particularly useful in recording cosmic rays (very high energy particles reaching the upper atmosphere from outer space).
  

Other kinds of particle detector simply register the passage of a particle through the apparatus and give no information about its path.  They are called counters.

• Scintillation counters use the fact that some plastic materials emit a flash of light when a charged particle passes through them.
• Cerenkov counters detect the characteristic electromagnetic radiation which is emitted when a charged particle moves through a transparent medium with a speed greater than that of light in the medium.
• Geiger counters are similar in principle to the spark chambers, but measure the current in the discharge rather than detecting the visible light from the spark.

All these detectors only detect charged particles.  Neutral particles must be observed indirectly, by the way they influence charged particles and by using conservation laws.

Link:

• Modern particle detectors
• Hands on Cern