As stated weightlifting requires most if not all muscles to some degree, however the snatch and clean & jerk are 2 different highly technical movements that use emphasis different muscles in different ways.
While strength training, like that suggested by Kate, is important, if you are interested in performing olympic weightlifting you may quickly find a program Starting Strength unsatisfying.
Starting Strength considers "the major lifts", i.e. the Bench Press, the Back Squat and the Deadlift, and trains these for maximal strength - moving the largest thing possible -, while olympic weightlifting trains for maximal force, what people refer to as an explosive movement or moving a relatively large thing as fast as possible.
Because of the slow controlled movements through a minimal plane, contemporary strength training may train minor auxillary, stabiliser muscles, but not to the degree in olympic weightlifting which requires controlling a large weight that is moving fast under going significant torque. Many athletes in contact incorporate at the least cleans into their programs for this reason.
If you are looking at doing olympic weightlifting, for fun or competition, its worth investigating what programs are available, beside the commonly suggested contemporary strength programs. Starting Strength will give you a good base, however if you are interested in olympic weightlifting supplementing it early on with technique practise of the major olympic movements - even with a broom handle.