The in-depth analysis above is the biggest help, for truly understanding the mechanics. For a simplistic approach (and you have probably already found something similar to this), this is how a friend of mine breaks it down for his own understanding (he recently broke 150k and admits that springs are his major weakness, but that this helps):
You want to watch for springs at either Kong's "foot" or Kong's "balls".
From the top of the ladder, once you are in good position to run toward the safe spot on the left of the final ladder, you want to run on a spring that bounces under Kong's balls. You have to wait for that spring to just barely clear you on its bounce, and then go. You also have to watch for the next spring. You want it to bounce at his balls also. If it does, keep going to the safe spot left of the final ladder. If it bounces at his feet, run back and repeat.
The opposite is true, in terms of the second spring, when running from the safe spot to the left of the ladder, to the final ladder. Again, you want to run on a spring that is at Kong's balls. Go as soon as the spring bounces over jumpman. If the next spring is also at his balls, run back. If it is at his foot, keep going.
Really, for the run up the ladder, the second spring just needs to be some position that is not equal to or greater than the position of the spring you ran on.
You will also find, with practice, you can a) cheat up the final ladder a smidge, and still have time to run back if the second spring isn't favorable, and b) have time to run back if you don't corner the ladder well and don't actually go up it (like I often do), if the second spring isn't favorable.
Hopefully this helps, and doesn't confuse further. I'm sure others have their own little tricks and techniques that help them be successful with the springs. For me, the springs were also the biggest learning curve impeding further upping my game from lucky L4 finishes to consistent L5+ finishes.
