The Olympic Lifts
Below is a general description of the snatch and the clean and jerk. These are not technical descriptions instead the descriptions are meant to give a brief illustration of what is going on with the lifts. If you are interested in learning the lifts I would recommend finding someone knowledgable or qualified in the lifts and having them teach you. And remember to maintain proper form.
The snatch is a more technical lift than the clean and jerk. Some people coin the snatch as the "fastest lift in the world" because is takes under 1 second to get the bar from the platform to overhead. A basic explanation of the snatch is the lifter will take a wide grip, for some this is almost to the collars of the bar, and will establish their grip on the barbell, usually a hook grip. Then the lifter will start the initial drive which comes from the hips, gluteal, and quadriceps muscles. The barbell will move upward and the torso will stay roughly at the same angle when the lifter set up. The lifter will then extend their body when the barbell reaches their pelvis. This hip extension will create enough force that it will propel the barbell upwards while the lifter drops underneath to catch the barbell. Then the lifter will recover and stand up with the barbell. This is the basic idea behind the snatch.
The Clean and Jerk
The Clean and Jerk is considered the ultimate test of strength and power for a lifter. The Clean and Jerk is broken into two parts, 1) The Clean and 2) The Jerk, but is still classified as one lift. The clean begins with a grip that is a little wider than shoulder width; this is mainly dependent upon the lifters preference. Then the pull begins which almost mimics a deadlift, but it is not technically a deadlift. The barbell will move up the body until it reaches about mid thigh for some, this is again mainly dependent on the size of the lifter, and at mid thigh the lifter will extend his body propelling the barbell upwards. As the bar is moving upwards the lifter will descend underneath the barbell and flip the wrists so the arms are almost parallel to the floor. The bar will then be racked across the front of the shoulders and will create what could be considered a shelf for the bar. The lifter will be in a front squat position and they will stand up with the barbell. That completes the clean portion of the lift.
The jerk immediately follows the clean. The lifter will bend their knees and dip and then straighten their legs propelling the barbell upwards. The lifter will push slightly with their arms and will be also pushed underneath the bar. The slight arm push is responsible for pushing the lifter underneath the barbell along with the lunging of the legs for the split jerk. There are numerous types of jerks, the split jerk, the power jerk, and the squat jerk. The most common type of jerk is the split jerk. Regardless of which version of jerk the lifter uses the lifter has to hold the barbell overhead with locked arms. If a lifter tries to push the barbell like a military press the lift will be disqualified. The photo below is of a split jerk.
Once again, if you are interested in learning the lifts then please try to find one nearby that will teach you. Otherwise if you are trying to teach yourself it's important to take it slow and cautious to make sure you get the form right.