You most likely did a push-up at some stage in your life before beginning CrossFit, but you may not have done the full spectrum of motion pushups we use in CrossFit. Your arms should be absolutely straight at the top, and your chest should be in touch with the ground at the bottom.
The most critical thing is to ensure that your core and shoulders are kept active to support your back and shoulder joints.
You will need to change your pushups before you start.
Instead of starting on your feet, work on your fingers, but position your hands on a box so that your upper body is lifted.
Start as high as you need to get your chest to the box for each pushup, and over time you can lower the box’s height before you finally take out the pushups on your toes at ground level like an army trooper!