There is a bit of a learning curve involved with regard to getting a perfect technique with these pushpins.
Like others have described, you have to undersrand first how it works.
Look on the top of each push pin, there's an arrow. When the pushpin is twisted in one direction, it will snap down and lock once it's pushed down. That's the direction they all have to be in when you're mounting it in. But first twist it in the other direction and pull the top all the way up, so that the black plastic pin is not inside the white clips on the bottom which actually grab the hole on the underside of the motherboard.
Now it's important to 'squeeze' the white plastic clips together if they have become worn and have come apart too far. If that happens, then when you go to mount it, one side of the clip will go in the hole and the other side can get squeezed between the heatsink and the motherboard and snap off. If you snap off a part of the clip, then you need to replace the whole mechanism. I have come accross heatsink assemblies that were installed improperly like this and had broken clips, and the customer was wondering why their computer was so slow (The CPU was throttling because of the poor contact)...
It's superior to a mounting bracket because you don't have to remove the entire motherboard to replace it.