Here are some examples.
"If the nuclear force were only a few percents weaker, then a proton could not combine with a neutron to form a deuteron. If this were the case, no deuterons would be formed in the sun and hence no solar fuel would exist. As a result, the sun would not shine (‘burn’), but would merely be a cold ball of inert gas—precluding the possibility of life on earth."
A slightly stronger gravity force would result in “a smaller universe of larger, brighter, shorter-lived stars, that will eventually collapse in on itself again in a Big Crunch. Most, if not all stars would be binary, trinary, or larger systems. Any planets orbiting these stars would have to go very fast to avoid a fiery demise inside their parent stars, and would be slung around wildly by their multiple suns. Any planetary system in this universe would be devoid of a stable, safe harbor for life, and relative stability is a vital prerequisite for the evolution of complex life forms. Life here would probably get to no more than amino acids, much less true life, before one of the planet’s parent stars went nova or the planet was torn apart and swallowed into one of the stars. It would not be a place to develop living creatures as complex as ourselves.”
There are different forms of the anthropic principle. The one form that most scholars agree upon is the Weak Anthropic Principle (WAP). This principle claims that conditions in the universe are such that they allow life to exist. If this statement did not impress you it is probably because we already know that the conditions of the universe are such that they allow for life by virtue of the fact that we exist. Thus everyone, including atheists and believers, agrees with the WAP so it can’t really be used effectively to argue for the existence of deity.
Then there is the Strong Anthropic Principle (SAP). The SAP basically states that because the universe must have certain properties for life to exist, and we exist, the universe was specifically designed or fine-tuned by a supreme being for the purpose of sustaining life. As a latter-day saint, I wholeheartedly accept the SAP premise, but it lacks rigor as an argument for the existence of deity with non-believers.
The problem with arguing that God lives because the universe we live in is fine-tuned for the existence of life is that we actually live in a universe that supports life. The very thing that gives rise to the argument for deity, namely a fine-tuned universe, also weakens the argument. Think of it this way. Imagine 5 universes where nature is fine-tuned to support human life. People in those 5 fine-tuned universes might marvel over the fact that their universes allow life to flourish, and some of them even propose a supreme being as their creator. Now imagine another 5 universes that are not fine-tuned to support life. In those universes no one is around to marvel over why their universes did not allow life to flourish because life cannot exist in them. A fine-tuned universe is all intelligent beings can ever know! So regardless of whether one is an atheist or a believer, there is amazement over the fact that life exists. To leverage this amazement by arguing that “therefore a supreme being must have created the universe,” carries little weight with atheists who are similarly amazed over the existence of our fine-tuned universe.
As a stand-alone rational argument for believing in deity, the weak and strong anthropic principles accomplish very little in the way of converting non-believers to the truth. But when coupled with the influence of the Spirit, anthropic arguments can suddenly make sense and facilitate conversion.