We can state the argument in the following way:
- We notice around us things that come into being and go out of being.
- Whatever comes into being or goes out being does not have to be; its nonbeing is a real possibility.
- Suppose that nothing has to be; that is, that nonbeing is a real possibility for everything.
- Then right now nothing would exist. For,
- If the universe began to exist, then all being must trace its origin to some past moment before which there existed – literally – nothing at all. But,
- From nothing nothing comes. So,
- The universe could not have begun.
- But suppose the universe never began. Then, for the infinitely long duration of cosmic history, all being had the built-in possibility not to be. But,
- If in an infinite time, that possibility was never realized, then it could not have been a real possibility at all. So,
- There must exist something that has to exist, that cannot not exist. This sort of being is called “necessary.”
- Either this necessary being belongs to the thing in itself or it is derived from another. If derived from another there must ultimately exist a being whose necessity is not derived, that is, an absolutely necessary being.
- This absolutely necessary being is God.
Perhaps this argument was a bit much in terms of trying to state something simplistically . Maybe this re-stated argument can be of some assistance:
- What we observe in the universe is contingent.
- A sequence of causally related contingent things cannot be infinite.
- The sequence of causally dependent contingent things must be finite.
- There must be a first cause in the sequence of contingent causes .
The argument basically runs as follows: We observe that things come in and out of existence – that is, they are contingent. More particularly, we notice things in the world that are capable of existing and capable of not existing. However, it is impossible for those contingent things to exist as such forever, for, anything that can fail to exist has not always existed. Since not all existents are capable of existing and not existing, there must be a necessary being – a being that cannot not exist. From this point, we are confronted with the question of whether or not this necessary being has its existence in itself or from another. As John F. Wippel writes in his essay on the metaphysics of Thomas Aquinas:
Every necessary (that is, incorruptible) being has a cause of its necessity from something else or its does not. One cannot regress to infinity with caused necessary beings. . . Therefore, he concludes, there must be a necessary being that does not depend on anything else for its necessity and that causes the necessity in all else. This being everyone calls God. 
What is important to notice with respect to this argument is its focus on two major steps: (1) the possible and (2) the necessary. Aquinas addresses these issues in separate fashions although they are headed under the same argument. In other words, the possible deals with contingent, or finite things. A finite thing, according to Winfried Corduan, meets any one of the following conditions:
- It is restricted by time and space.
- It can be changed by something other than itself.
- It has a beginning in time.
- It needs things other than itself to continue existing.
- Its attributes, whether essential or accidental, are to some extent influenced by other things. 
It is not the case that something is caused, sustained, shaped and etc. and is contingent. Rather, it is these very attributes that make something contingent. However, crucial to Aquinas’ argument is the claim that “Unless there were an infinite being, there could not be an finite beings.” This goes to expose the inherent and crucially important metaphysical element in Aquinas’ argument that is often ignored. In other words, “[A]s surprising as this may sound, there have been numerous attempts either to state or to refute the cosmological argument without doing metaphysics” . Vital to Aquinas’ argument is Aristotle’s explanation of being. Perhaps the best summary of Aristotle’s explanation comes from an essay by Joseph Owens:
Everything encountered in our perception is known as a being. If it happens to be metal, a plant, an animal, or a human person, it is a substance. If it is a color, a size, or a relation, it is an accident and requires a substance in which it inheres. If it is right there before our eyes, it is actual. If it is to come into being in the future, it is still something potential and requires efficient causality to make it actual. If it undergoes change, it is temporal and is composed of matter that changes from one form to another. When we reason to things that have no matter and therefore no potentially for change, we consider objects that are merely being, in contrast to becoming and perishing. They are the primary instances of being. All other things are beings focal reference to them. 
Now, the efficient causality (“the primary source of the change”) with respect to the universe is different in Aristotle’s thought than it is in Aquinas’. Aquinas’ approach to this Aristotelian conception of being was particularly that God was the efficient cause of all things, and not so much that the universe “originated in motion” rather than was “bestowed existence”. According to Owens with respect to Aquinas’ position, “God was the primary instance of being. His was the nature to which all other beings had focal reference as beings” .
However, let’s back up a little bit towards the conversation of change. Aristotle argued through a metaphysical scheme that essentially said that since absolute nonbeing does not exist, therefore the reality of change must occur somewhere within being. Hence, we have two further given realities: (1) Change is real, and (2) change occurs in the realm of being. Given this, there must be two kinds of being: (a) being that currently is (actual), and (b) being that will be when the change occurs (potential). These terms were discussed in that passage by Joseph Owens above. To quote him again, “If it is right there before our eyes, it is actual. If it is to come into being in the future, it is still something potential and requires efficient causality to make it actual” (emphasis mine).
Change and motion then can be understood with respect to these two terms. “Motion” is thought to be the change from potentiality to actuality, while “change” is the actualization of a potential. In the former case, it is similar to Newton’s first law motion in the sense that change will not take place until some other external factor interferes . In the latter case, change simply means that a causal agent imposes a different form on a substance. For instance, a lump of clay has the potential of becoming a bowl if there is a potter to actualize that potentiality. The potter functions as the causal agent, while the bowl now represents a different form of a given substance – namely, the lump of clay.
However, an important factor to this whole metaphysical scenario is that this causal agent itself be actual. In other words, you cannot actualize the potential (i.e., change) of something that does not exist, and furthermore that something already actual must function as its cause. That is to say, potentials do not actualize themselves. Thus, the case is this: “finite beings are actualized potential and… it takes a cause, which is an actual being in its own right, to actualize the potential” . However, we need to have a proper understanding of causality.
It is not the case that we understand there be some event A which is followed by another event B, which is followed by some other event C and so on and so on. This form of causality was attacked by David Hume on the basis of its “mysterious indemonstrability” and reveals the inherent problems of understanding causality in this way. Rather, we may understand cause-effect to function so as to say that cause is only understood insofar as there is a change in the being of the effect. To use an explanation from Timothy McDermott:
The existence of the cause expresses itself in activity, but that activity is the coming to existence of the effect. Causality, then, should not be given the modern reading involving a sequence of two changes: it is one change in the effect as seen from the cause. 
- (a’) A contingent being is one that requires a cause to exist.
Hence, whatever exists contingently never ceases its requiring of a cause. This leads us back to our earlier statement so as to say, that “Unless there were an infinite being, there could not be any finite beings.” This infinite being must have the following conditions:
- It is not restricted by time or space;
- that cannot be changed by anything other than itself;
- that did not have a beginning in time;
- that does not need things other than itself to continue existing;
- whose attributes are not influenced by other things (which means that it only has essential attributes, not accidental ones).
This infinite being seems to be of the kind that we usually refer to as God.
-  Although, I still nonetheless find the scheme helpful. It was taken from Peter Kreeft and Ronald K. Tacelli, Handbook of Catholic Apologetics (Ignatius Press: 1997) pp. 57-58
-  This was taken from W. David Beck, “A Thomistic Cosmological Argument” in To Everyone An Answer, ed. William Lane Craig, Francis Beckwith, J.P. Moreland (IVP Academic: 2004) pp. 99-100
- John F. Wippel, “Metaphysics” in The Cambridge Companion to Aquinas, ed. Norman Kretzmann and Eleonore Stump (Cambridge University Press: 1997) p. 115
-  Winfried Corduan, “The Cosmological Argument” in Reasons for Faith, ed. Norman Geisler and Chad Meister (Crossway Books: 2007) p. 204
-  Ibid., p. 203
-  Joseph Owens, “Aristotle and Aquinas” in The Cambridge Companion to Aquinas (1997) p. 45 – emphasis mine
-  Ibid., p. 46
-  Newton’s first law: “Every object in a state of uniform motion tends to remain in the state of motion unless an external force is applied to it.”
-  Winfried Corduan, “The Cosmological Argument” in Reasons for Faith (2007) p. 211
-  Timothy McDermott, “Existence and Causality,” Appendix 3, ST, (McGraw-Hill: 1964) p. 184