Question: How does observation of, say the Five Precepts (of not killing, stealing, having sexual misconduct, lying and taking of intoxicants) rid the Three Poisons?
Answer: Since all precepts are broken only due to giving in to the three poisons, the precepts when observed serve as preventive measures. In this sense, mere observation of the precepts does not rid the poisons, but limit their expression and proliferation.
This is where Nianfo comes is as an important complementary practice, to disempower and dissolve the poisons instead of just suppressing them. Here is an article on how Nianfo purges the poisons, by reconnecting directly to our pure Buddha-nature (which is free of all poisons) with Amituofo’s assistance: http://purelanders.com/2016/02/24/how-does-nianfo-eradicate-our-five-poisons
The more committed we are to observing the precepts well, the easier it is to Nianfo well. This is while the more sincerely we are in Nianfo practice, the easier it is to observe the precepts well. There is a direct mutually and simultaneously supportive relationship between the two. Within the Threefold Training (三学) for liberation, of Precepts (戒), Concentration (定) and Wisdom (慧), the first two are so closely intertwined that they are often mentioned together (as 戒定) too. When we practise Nianfo, we are cultivating all three aspects, not just the first or first two, as we can see at http://purelanders.com/2011/12/17/buddha-mindfulness-as-threefold-training