The Cosmological Argument is not one argument, but rather a group of several arguments for the existence of God proposed by different thinkers over the centuries. Here is one relatively simple form of it – just 2 premises and the conclusion – but with a lot packed in those 2 premises, and a serious implication inferred by the seemingly modest conclusion. Whole books can be written on each point, but in a nutshell, it goes like this:
Premise 1) Whatever begins to exist has a cause.
Premise 2) The universe began to exist.
Conclusion) Therefore, the universe has a cause.
Premise 1 is simply the law of causality, (i.e. cause and effect): the effect (beginning to exist) has a cause. This law is not only fundamental to science, but also verifiable by anyone through our everyday observations. Nobody walks into a room and, seeing a ball rolling across the room, assumes the ball has always been in motion. We instinctively look in the direction the ball rolled from to see who or what caused it to roll. Notice that this premise does not say that whatever exists has a cause, but that whatever begins to exist does. If either the theist’s God or the atheist’s universe is eternal, then neither would require a cause. Hence the atheist’s question of “Who made God?” is as irrelevant as asking them who made the universe in their view. No one needed to. That’s the nature of anything being eternal.
But Premise 2 then eliminates the option of an eternal universe through three independent lines of reasoning: one scientific and two philosophical. First, a host of scientific evidence points to the universe having a definite beginning. The Standard Cosmological Model (the “Big Bang”), whether you agree with the specifics of it or not, has withstood decades of attempted refutation and points to a unique beginning to all space and time at a single point in history, a singularity where space and time cease to exist prior to that point. Another insurmountable obstacle is the 2nd Law of Thermodynamics. This is the most universally accepted physical law, so much so that it forms the basis of the US Patent Office refusing to grant patents for perpetual motion machines without a working model. As Sir Arthur Eddington said, “if your theory is found to be against the second law of thermodynamics, I can give you no hope; there is nothing for it but to collapse in deepest humiliation.” The universe is only winding down. But if it is only winding down, that means it had be wound up.
Attacking the possibility of an eternal universe philosophically, we have two more abstract, but nevertheless valid, approaches. First, an eternal universe would require an infinite regress, but there can be no actual infinite regress because an actually infinite number of things cannot exist. A beginningless series of events in time entails an actually infinite number of things (events in this case). Therefore, a beginningless series of events in time cannot actually exist.
The second philosophical rationale is that one cannot traverse an infinite series. The series of events in time is a collection formed by adding one member (or event) after another. A collection formed by adding one member after another cannot be actually infinite. So then, the series of events in time cannot be actually infinite.
Therefore, the universe has a cause. If this argument seemed fairly noncontroversial to you right from the beginning, then you might be surprised at the resistance to it. That’s because of the implications the conclusion leads us to. This cause cannot be material or temporal as space and time both had a beginning, and this first uncaused cause would necessarily have to exist before the effect it caused (the universe). This cause must be extremely powerful to cause everything observable (and probably more that we haven’t observed). The incredibly detailed precision observed in the universe would require an intellect far beyond the greatest human minds to orchestrate the intimately interrelated web of cause and effect detected so far. For comparison, we routinely fail to predict the consequences of even simple actions over periods of days or weeks (i.e. weather prediction). This cause is necessarily a free agent capable of making choices. An impersonal force like gravity cannot choose to act at a particular time on an object. A ball does not simply float in the air until gravity decides to act on it and make it fall to the ground. If this cause were simply a force like gravity, acting from all eternity, then the effect (the universe) would be eternal as well, which contradicts the observed evidence and our reasoning. This cause is therefore a person, in the general sense of a being possessing rationality. This first cause, or uncaused cause, then appears to be, for all practical purposes: eternal, omnipotent, omniscient, and personal. As with the Ontological Argument from last week, this correlates well with the description of God in the Bible and forces us to face the possibility of a sovereign Maker who might very well hold us accountable for our actions. Hence, the determined resistance to this line of reasoning.
 See “Reasonable Faith”, 3rd Ed., chapters 3 & 4, by William Lane Craig for a much more detailed treatment of this and other arguments for the existence of God.
 Sir Arthur Eddington, “The Nature of the Physical World”, 1927.