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 √ s = 1.96 TeV pp 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.ii Acknowledgements I feel the deepest respect for my advisor Sunil Somalwar. I want to thank him for being a friend, a philosopher, and a guide in the truest sense of those words. Without him, I would not love particle physics; it is as simple as that. and Bob Stone who made sure that the computers work, the CAF runs smoothly and helped me with the day-to-day questions to which I wouldn't know where to find answers. Thanks to Nancy DeHaan for shielding me from the administrative quicksands.The trilepton analysis would not be any fun without Anadi, Else, Giulia, John, and Vadim.Working with them ensured that even the most annoying tasks were enjoyable. I want to thank them for all their guidance, scripts, code, and conversations. The convenors at CDF also deserve a special mention; Ben, Chris, Dave and Monica. They taught me to think carefully, do a good analysis, give a good talk and much more.iii Tim Koeth and Rouven Essig helped to make Batavia and Piscataway as much of a home as Pune is; for that I'm grateful. Between them, I'm sure they will cover the best of experiment and theory and it is a privilege to know them.The last two years have been made special by Aditya and Sarika, Amit and Diptee, Mandar and Shreya, Pankaj and Prajakta, Shreedhar and Meenal, and Salil. The good times we have had together has made sure that the evenings I had for my own were well spent. They have been a sounding board for my wildest ideas, and they have been patient with me.