One of the most obvious applications of progressive overload is with strength training. I'm almost certain that no one has ever made any made any gains doing 10 push ups a day all their life.
Eventually their gonna have to do 7, know what I mean??
With your strength training there are plenty of things you can do to progressively increase the intensity of your workout, that doesn't always limit you to adding more weight. You can take away a limb to change your base of support, you can perform the move on the balance pad, you can perform the move using different equipment and the list goes on...
OR...
Of course, you can just increase the weight. For most people increasing your weight about 5lbs per week on upper body exercises and 10lbs per week for lower body exercise will help you progress at a nice pace.
And really, with increasing the weight by 5lbs or 10lbs I'd only do that for 1-2 exercises out of the workout per day. You definitely want pick one of your prime compound movements and maybe an isolation exercise.
Another thing to keep in mind with strength training is that you want to build you strength focusing on one element of strength. For beginners you'll have to work on building the strength to stabilize yourself. From there you can build the strength needed to control and decelerate forces, then work into building up your maximal strength.
The most important thing to remember about all of this progressive over load talk is that it is PROGRESSIVE overload. It's really easy to get ahead of yourself especially when the strength gains are going up like crazy. There comes a time where those numbers kind of level off and you have to know how to react to it.
It's really not worth developing any messed up movements patterns that could cause you an injury today or later on down the line.