The following is Robin Collins’ fine-tuning argument for the existence of a fine-tuner I used in the VT debate on the existence of God. This version of the fine-tuning argument is an abductive version. I believe this argument, when used in an abductive form, is the strongest form of the argument. You’ll usually see it in a deductive form, a la William Lane Craig. For my method of argumentation please see: VT–My Method of Argumentation.
The fine-tuning argument argues that when the physics and the laws of nature are expressed mathematically their values are ever so balanced in a way that permits the existence of life. This claim is made on the basis that existence of vital substances such as carbon, and the properties of objects such as stable long-lived stars, depend rather sensitively on the values of certain physical parameters, and on the cosmological initial conditions. I’m merely arguing that the universe/multiverse is fine-tuned for the essential building blocks and environments that life requires for cosmic and biological evolution to even occur.
- Given the fine-tuning evidence, a life permitting universe/multiverse (LPM) is very, very epistemically unlikely under the non-existence of a fine-tuner (~FT): that is, P(LPM|~FT & k’) ≪ 1.
- Given the fine-tuning evidence, LPM is not unlikely under FT (Fine-Tuner): that is, ~P(LPM|FT & k’) ≪ 1.
- Therefore, LPM strongly supports FT over ~FT. 
*Remember, k’ represents some appropriately chosen background information that does not include other arguments for the existence of God while merely k would encompass all background information, which would include the other arguments, and ≪ represents much, much less than (thus, making P(LPM|~FT & k’) close to zero).
The argument is valid since the conclusion follows from the premises.
Why think the fine-tuning evidence is very, very unlikely under a non-fine-tuner hypothesis? Single universe scenarios require the fine-tuning of the laws of nature, the fundamental constants, and the initial conditions of the big bang in order for life to exist. The list of necessary parameters is quite extensive (such as the fine-tuning of the strong and weak nuclear forces, the cosmological constant, electromagnetism, etc.). However, the most common reaction to the fine-tuning argument is to appeal to 1 of 4 different types of multiverse scenarios with three of those suggesting that our Hubble volume is one amongst countless others with these other universes having different physics. However, these multiverse scenarios require just as much of an explanation as a single universe. The inflationary/superstring multiverse scenario can only produce life-sustaining universes because it has the following four components/mechanisms.
- A mechanism to supply the energy needed form the bubble universes: The fine-tuning of the inflation field
- A mechanism to form the bubbles.
- The actual mechanism is Einstein’s field equations + inflation field. The inflation field that gives empty space a positive energy density is needed to achieve these first two components. Without either factor, there would neither be regions of space that inflate nor would those regions have the mass-energy necessary for a universe to exist. If, for example, the universe obeyed Newton’s theory of gravity instead of Einstein’s, the vacuum energy of the inflation field would at best simply create gravitational attraction causing space to contract, not to expand.
- A mechanism to convert the energy of the inflation field to the normal mass/energy we find in our universe.
- The actual mechanism is E=mc2 + coupling between the inflation field and matter fields. The conversion of the energy of the inflation field to the normal mass-energy of our universe is achieved by Einstein’s equivalence of mass and energy (E=mc2) along with the assumption that there is a coupling between the inflation field and the matter fields.
- A mechanism that allows enough variation in the constants of physics among universes (one of the predictions of quantum cosmology is random constants).
- The actual mechanism is superstring theory or M-theory. Although some of the laws of physics can vary from universe to universe in M-theory, these fundamental laws and principles underlie M-theory and therefore cannot be explained as a multiverse selection effect. Further, since the variation among universes would consist of variation of the masses, and types of particles and the form of the forces between them, complex structures would almost certainly not be atomlike and stable energy sources would almost certainly require aggregates of matter. Thus, the said fundamental laws seems necessary for there to be life in any of the many universes, not merely in a universe with our specific types of particles and forces. 
In defense of premise 2, the best scientific evidence does suggest fine-tuning. The fine-tuning hypothesis is a religiously neutral position. The question is whether it is more reasonable to infer the existence of a fine-tuner to produce a product that exhibits fine-tuning or whether this happened by chance. Andrei Linde recently published a paper suggesting that there are 1010^10^7 universes in the multiverse landscape as a product of slow-roll inflation. We know at least one universe that exhibits life that may have been randomly produced. Or, this could be a product of nomic necessity but there doesn’t seem to be an account for explaining the nomic necessity as a logical or metaphysical necessity. A strong case would have to be made.
The conclusion follows logically from the premises. This gets us to an extremely intelligent agent. Whether there is one universe or a sea of universes in the multiverse landscape the fine-tuning evidence must have an explanation. Thus, the evidence of the fine-tuning we observe, the values of constants and laws of nature, the initial conditions, the inflation field, Einstein’s equations, and string theory itself is much, much more likely under the hypothesis that there is a fine-tuner.
 Ibid. 263-67.
 Andrei Linde and Vitaly Vanchurin, “How many universes are in the multiverse?” http://arxiv.org/pdf/0910.1589.pdf (accessed March 11, 2011).