What you do first is read the instructions.
In case they're missing, this is how it works: this type of strap-lock is released by pushing the button in the middle, unlike the Schaller type where you pull to release.
When you've separated the components, the saucer-shaped part goes on the outside of the strap with the actual lock passing through the middle of it, through the hole in the strap. Turn the strap over and place the big flat washer over the lock, then secure with the circlip in the machined groove in the body of the lock. Depending on how thick the strap is, this can be easy or tough to do, but make sure the clip is properly seated and fully home - square-nose pliers can help but take care not to damage the lock.
Once the assembly is completed correctly it will never loosen by itself; I've heard that the other screwed-together type has been known to do that.
The button screws provided are bigger and longer than the regular kind and quite hard to drive in by hand. Very secure, but experience has led me normally to re-use the regular button screws (provided they were good and tight to begin with), while keeping an eye open for any signs of loosening in use. If this does happen you can then use the bigger, longer ones instead.