Catholic Ecology offers a good template for evangelizing those with no religious affiliation:
In beginning the conversation with beauty, goodness, and truth, one opens a dialogue that can then reverse the order of those transcendent realities. In calling attention to shared understandings of the beauty and goodness of creation, one can then speak of the truths of creation—of natural laws. From there, one might acknowledge that absolute truths exist. One may then be able to speak of a Truth. From there, one might suggest that this Truth is a Person, because this Truth is, ultimately, sacrificial love. And love is never impersonal.
Catholic intellectual and spiritual tradition holds that we can know something of the Creator through studying creation. In speaking to those who do not embrace the Christian creed, the Holy Father first spoke about the very essences of human dignity and the very nature of nature. By simply beginning this conversation, he laid a path for unbelievers to follow, should they wish.