As a part of basic reminders, it is worth the effort to read and watch how Robin Collins put the case in summary, in a classic essay on The Fine-tuning Design Argument (1998):
Suppose we went on a mission to Mars, and found a domed structure in which everything was set up just right for life to exist. The temperature, for example, was set around 70 °F and the humidity was at 50%; moreover, there was an oxygen recycling system, an energy gathering system, and a whole system for the production of food. Put simply, the domed structure appeared to be a fully functioning biosphere. What conclusion would we draw from finding this structure? Would we draw the conclusion that it just happened to form by chance? Certainly not. Instead, we would unanimously conclude that it was designed by some intelligent being. Why would we draw this conclusion? Because an intelligent designer appears to be the only plausible explanation for the existence of the structure. That is, the only alternative explanation we can think of–that the structure was formed by some natural process–seems extremely unlikely. Of course, it is possible that, for example, through some volcanic eruption various metals and other compounds could have formed, and then separated out in just the right way to produce the “biosphere,” but such a scenario strikes us as extraordinarily unlikely, thus making this alternative explanation unbelievable.
The universe is analogous to such a “biosphere,” according to recent findings in physics . . . . Scientists call this extraordinary balancing of the parameters of physics and the initial conditions of the universe the “fine-tuning of the cosmos” . . . For example, theoretical physicist and popular science writer Paul Davies–whose early writings were not particularly sympathetic to theism–claims that with regard to basic structure of the universe, “the impression of design is overwhelming” (Davies, 1988, p. 203) . . .
[Cf. also here. Short summary here. Elsewhere, Collins notes how noted cosmologist Roger Penrose has estimated that “[i]in order to produce a universe resembling the one in which we live, the Creator would have to aim for an absurdly tiny volume of the phase space of possible universes — about 1/(10^(10^123)) of the entire volume . . .” That is, 1 divided by 10 followed by one less than 10^123 zeros. By a long shot, there are not enough atoms in the observed universe [~10^80] to fully write out the fraction.]
A video summary by Robin Collins (NB: a low-res sample from a DVD Product available from http://www.arn.org. This program was recorded at the “Intelligent Design and the Future of Science” conference held at Biola University, April 22-24, 2004):