To detect means to establish a situation (an experiment) in which the 'elementary particle' in question interacts with the system (or particles in the system), or as BenLillie indicated, fundamental particles (electrons) or composites (e.g. protons, composites of quarks) can be collided. The result of that interaction is 'detected'.
The elementary particles are the 'smallest' individual particles, e.g. leptons like the neutrinos and electron (positron), quarks (which make up mesons and baryons), and then others like gluons, bosons, gravitons, . . . . The latter group is much harder to detect, and must be inferred indirectly from the particles that are detected.
From the link provided by BenLillie -