How to Progress Push Ups
Push ups are a universal exercise, but they are commonly messed up. Many people don't realize there are ways to regress them to any activity level.
A traditional push up is roughly 2/3 of your body weight. An easy way to work to being able to do push ups is to develop your push/press strength to that benchmark for reps. So bench press or dumbbell bench press. If you don't have access to that, here's a guide to work on them.
#1 Hands elevated push up
Push ups on your knees can work, but I like this variation more since it forces you to control your body. The angle can be manipulated based on your ability. Can barely get any - use the wall. Pretty good at them? You can use couch height.
If you can do 15-20 full ROM reps from any height, i'd say go ahead and lower yourself.
What about knee push ups? These are an okay subsitute, but I prefer the hands elevated because it forces you to stiffen up the entire body, something that will translate to a regular push up in the long run.
#2 Regular push ups
Won't spend too much time here, just note the elbow position. Try to use this for every variation. Be an ARROW, not a T.
#3 Feet elevated push ups
If you can easily rip off 20+ regular push ups, move to feet elevated. How high you elevated your feet depends on your strength level, but I prefer a height that allows your chest to be on the ground without a big sag in the low back. The higher the feet, the less depth you can get without all kinds of weird low back compensations.
Sets of 15-20 is a good target.
Summary
These are my favorite push up progressions. You can get created with plyo versions, different hand placements, and all that jazz, but get good at these basics and you'll be fine. I like that 15-20 rep sweet spot, you could even shift that up to 30.