We have talked about many push up variations here. One of the best for beginners is the side to side push up. There are a few versions of this push up.
Start in the push up position with arms slightly wider then shoulder width apart. Begin to lower yourself to the ground but lean to your left side so that your left pectoral comes close to touching your left hand. Push yourself back up and complete a similar movement but toward your opposite hand. Attempt to be able to do 20 reps to each side. Once you have mastered these variations consider raising a leg or adding a weighted vest to increase tension and difficulty.
A variation on this is to slide from one hand to the other once you have lowered yourself. The individual in the below video shows a perfect example of how to complete these two variations.
This movement sounds easy and not much of a change however you will notice the result right away. If this is your first time trying this you will feel the burn in your pectoral by the third rep. This is because you are putting almost all your weight onto one side of your body and this is causing that pectoral to lift the load. This is good because it is not a complete unilateral movement so your body has stability but at the same time it is working one side harder then the other. This will correct any weaknesses while building additional strength.