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We review the use of optical spectroscopy, electron-induced radiation emission (cathodoluminescence), and electron energy-loss spectroscopy to study localized surface plasmon excitations in sub-wavelength noble-metal nanoparticles prepared via lithography or colloidal chemistry. These techniques provide information about plasmon excitations by recording different physical processes, specifically, light scattering exerted by the particles on externally incoming light, radiation emission produced by interaction with an electron beam, and energy loss suffered by those electrons. We provide a theoretical description of a study of the spectral features and spatially resolved maps of nanoparticle plasmon modes at the single-particle level by using these techniques. Numerical modeling is carried out for each set of experimental measurements in order to interpret the results.