There's no one method of Quarantine. With mutants who can have bizarre abilities or resistances, some ways may not be effective in some cases. The following here are general guidelines:

• The less change a mutant has to fight you, the better. As such, in all cases, poisoning (or drugging beforehand) is an extremely preferable method of Quarantine. Some poisons can be hard to trace (though they won't be listed here for certain legal reasons, they can be discovered through a little research or sometimes through asking other Final Quarantine members) and may not cause much suspicion, especially if you can refuse an autopsy on some grounds. Asphyxiation is also effective, but can lead to more questions.
• Making it look like it was self-inflicted is also a good idea, but can be tricky to pull off and should someone be suspicious usually evidence can be found against it. If police are sympathetic to Quarantine standards, but not willing to outright help, this is often the best way to go about things.
• Failing that, any means that work are acceptable
• In all cases, it's important to try to hide your belief in the Quarantine from all children, known to be contaminated or not. If they know what is necessary to do to them, they're more likely not to tell you if they discover they are contaminated, and you'll miss your chance. They may run and then they will become monsters that much quicker. The best approach, if you're not a good enough actor to pretend to accept mutants, is to stay carefully silent about your stand on mutant issues near children, although some may confess their contamination to you even if you're vocally fearful of mutants.