This dissertation describes a search for the associated production of the supersymmetric particles, the chargino and the neutralino, through their R-parity conserving decays to three leptons and missing energy. This search is carried out using the data collected at the CDF experiment at the Tevatron (radical)s = 1.96 TeV p(bar p) collider at Fermilab. The results are obtained by combining five independent channels with varying signal to background ratio. Overall, a total of 6.4 (+-) 1.1 background events from standard model processes and 11.4 (+-) 1.1 signal events for a particular choice of mSUGRA model parameters are expected. The observation of 7 events in data is consistent with the standard model background expectation, and the mSUGRA model is constrained. Limits are set on the cross section of Chargino-Neutralino pair production, and a limit on the mass of the chargino is extracted. A method of obtaining model-independent results is also discussed.