You should begin strengthening at a level in which you can do quality reps while maintaining proper posture. Depending on your level, you can start as easy as on a wall. You can challenge yourself further by moving down lower to a counter, table, or chair. The eventual goal is being able to get all the way to the ground. Whatever level you can successfully do at least one rep at with maintaining proper posture should be considered your current strength level. Your stability level will be at least one level beyond your strength level. So this means you should perform isometric planks at a level lower to the ground than your current strength level. For example, if your current strength level only allows you to do pushups on the wall, you should perform planks on a counter. For the planks you will want to hold and stabilize a posture for a period of time. Some good schemes to use would be 3 sets of 30 seconds, or 10 sets of 10 seconds. As you get stronger continue to move your way down towards the ground for pushups, while performing planks at one level closer to the ground than your pushups.
Now, once you are able to successfully perform planks from the ground, maintaining proper posture for at least one set of 30 seconds, you can begin modified pushups from the ground. The first modified position is actually starting with your body all the way on the floor. Instead of starting from lockout, or top plank position, start from the ground, push yourself up to your knees, and then lift your knees up into plank. Once at the top lower yourself under as much control as possible maintaining proper posture until you are all the way on the ground. If you start off “flopping” on the floor, this is quite ok, just maintain control for as long as possible. As you get stronger you will be able to lower yourself with more and more control. Also as you get stronger, on the up part of the pushup, you will be able to spend less and less time on your knees. Try to more quickly transition from knees to plank until you barely need the knees at all. Pretty soon after, as you can lower yourself under control and not need your knees intermediately on the way up, you will be able to start from the top position and do a full pushup! Using this method will best train the core along with all the other upper body muscles to best teach intramuscular coordination, and get you pounding out plenty of proper pushups.
Another key thing to remember is that this is a training process. Everybody will start at different parts of the training spectrum. It is not about where your start however, it is about where you end up. It will take plenty of time and work, but anybody, at any level can train to be able to do better pushups.