Why would European countries extradite american criminals to the US? Because we established a trust in each other and want to keep it that way for both sides benefits.
How are these treaties enforced? All international treaties are ultimately based on trust. There is no higher authority, only elective councils of and voluntary commitment to procedures (a.k.a. promises) by sovereign states.
Specifically not even these formal promises have been given by e.g. the United States of America which to this day has signed but never ratified either the VCLT[1] or the VCLTIO[2], so is figuratively giving a lukewarm "let's see about the convenience of that when it comes up".
1: https://en.wikipedia.org/wiki/Vienna_Convention_on_the_Law_o...
2: https://en.wikipedia.org/wiki/Vienna_Convention_on_the_Law_o...