The pushup is one of the oldest body weight exercises and can be a huge benefit to core and total body strength, but performing it correctly is the key to achieving those benefits.
The pushup starts with the body in the prone position with feet together. Hands should be flat on the floor pointed forward and under the shoulders. From this position, push the body off the ground until the arms are straight. Once you are completely up, you will reverse the process and slowly lower your body back down toward the floor.
In the pushing phase, movement happens at the elbow, shoulder and scapular joints. In the elbow, extension occurs, in the shoulder joint, horizontal adduction occurs and at the scapular joint, scapular abduction occurs during the pushing phase. In the lowering phase, the same muscles that work in the pushing phase are active, but this time eccentrically. It is important to keep the core engaged at all points during the pushup to ensure the low back does not sag to the ground.
The more you train the body to perform a pushup, the easier the motion will become and the more strength you will build. Start with 1 set of pushups to failure (even if that means one) 2-3 times a week. Continue this process until you are able to correctly perform 10 consecutive pushups (or more if you have a set goal).