One of the girls on my basketball team is going to the military in a few months. She asked me how to up her pushup count for the PFT. My first thought was do them properly and utilize your whole body instead of just your lowly little triceps (which most guys do)! Done properly, the pushup is a compound exercise that uses muscles in the chest, shoulders, triceps, back, abs and even the legs.
So I wanted to go over some pointers for getting the most out of your pushups, so maybe you can gain the strength and power to do some of the variations in that viral workout video where that military guy shows some of the most insane bodyweight exercises.
And now on with the show…so first thing you need is a good starting position. Start by getting onto the floor with your hands directly below and even (ever so) slightly wider than your shoulders. 
*Side note if you’re chest muscles are unable to handle the load you will more than likely try to inch your hands forward above the plane of your shoulders (meaning if looking from the top your thumbs would be more in line with your nose than your collar bone).
Now straighten your legs and press your heels to the back. I like to have folks place their heels on a wall and keep them there throughout the movement (harder than it sounds). Also squeeze your bum (like a stripper with a $20). By activating your legs and tightening your tush in conjunction with abdominal engagement you will help keep your lower back from arching.
You are now in a plank position, be sure you keep a straight line from your ears, to your ankles. It occasionally happens that people will drop the head as they lower into the pushup position (as if nodding yes) this happens if either from lack of chest strength, poor posture in general, or lack of knowledge. We sometimes see this with the hip area as well (as if #@!ping the floor), you want to keep your hips in line with your torso to fully engage your abs.
Lastly we talk about the hands/wrists and elbows as they bend to perform the pushup. When you are holding the plank as well as performing the pushup place the weight of your body on the outsides of your hands and not the bottom (or wrist area). The outside is a more stable stronger surface and can handle the work/abuse.
As far as the elbows they should bend and angle back about 45-60 degrees and not directly out to the sides at 90 degrees. 
In other words, if looking from the top your arms would angle back like a grasshopper and not flare out to the sides (in a straight line elbow to elbow).
Alright, so we’re cool on pushups then right? Sweet, if you have any questions or topics you would like me to cover just let me know…you’ve got questions; Ive got something to say about it!! Ha ha
We’ve got fancy new things on the horizon for TBT, get in on the ground floor. Ciao