I'll disregard the emphasis on monks, because mindfulness isn't exclusive to monastics, and secondly, the monk as a super-hero trope needs some critical examination. Most monks, like 90% of them in traditionally Buddhist countries follow the herd, and ordain because it is better than farming, or because their family gets some respect in the village, or some motive other than nibbana and buddhahood. This means, it is the rare monk generally that graduates to being a real super hero in the sense of an Arhat, or who can practice or even attempt 100% mindfulness. This doesn't mean the rest of them are bad monks, not at all. Monks are human after all, and they are attempting the near impossible, which is more than one can say of most. Even in the time of the Buddha, there were a good many monks who were earnest at least initially, but were not so special, it appears.
I say all this because I respect and love the idea of monasticism, and don't want to see it become a Potemkin village. I live in India, where the popular notion of a monastic (Hindu, Buddhist, what have you) has taken a real beating, and a monastic is viewed by the urban educated as a sex and money crazy conman. There are still enough of course who unquestioningly fall at the feet of anyone in saffron robes, but that isn't very healthy either.
Politicians all claim to be incorruptible because no one votes for the one who is honest enough to admit he is a little dirty, because politics in general is a little dirty. And, monks and dharma teachers are similarly forced to at least tacitly let on that they are beyond simple human frailties, at least the really bad ones, and they constantly endeavor to live in mindfulness and bliss and speak in soothing voices.
The love of Nibbana cannot be born out of a hatred for anything, not even Samsara. In fact there cannot be Nirvana without Samsara, they inter-depend.
The old Zen saying is when sleeping sleep, when showering shower, when walking walk. This no-mind state is easier said than done.
By being regular in one's schedule and routine, and by having a time set apart each day to meditate one can bring about mindfulness.
Meditating daily or regularly, and attaining jhanas often is another good way to ensure constant mindfulness.
Being in the presence of an enlightened teacher who radiates mindfulness is yet another way to boost our own mindfulness energy.
Regular and heartfelt practice of Metta is another way to increase mindfulness.
Making a habit of returning to the present moment, is another good way. See, Thich Nhat Hanh's mindfullness moment practice
Not dwelling in negative thoughts and practicing the Bramha viharas is another method.