The following selection consists of the "Five Ways" which is a small portion of the Summa theologiae.

Article 3: Whether God exists.
Thus we proceed to the third point. It seems that God does not exist, for if one of two contrary things were infinite, its opposite would be completely destroyed. By "God," however, we mean some infinite good. Therefore, if God existed evil would not. Evil does exist in the world, however. Therefore God does not exist.

 Furthermore, one should not needlessly multiply elements in an explanation. It seems that we can account for everything we see in this world on the assumption that God does not exist. All natural effects can be traced to natural causes, and all contrived effects can be traced to human reason and will. Thus there is no need to suppose that God exists.

 But on the contrary God says, "I am who I am" (Ex. 3:14).

 Response: It must be said that God's existence can be proved in five ways.
The first and most obvious way is based on the existence of motion. It is certain and in fact evident to our senses that some things in the world are moved. Everything that is moved, however, is moved by something else, for a thing cannot be moved unless that movement is potentially within it. A thing moves something else insofar as it actually exists, for to move something is simply to actualize what is potentially within that thing. Something can be led thus from potentiality to actuality only by something else which is already actualized. For example, a fire, which is actually hot, causes the change or motion whereby wood, which is potentially hot, becomes actually hot. Now it is impossible that something should be potentially and actually the same thing at the same time, although it could be potentially and actually different things. For example, what is actually hot cannot at the same moment be actually cold, although it can be actually hot and potentially cold. Therefore it is impossible that a thing could move itself, for that would involve simultaneously moving and being moved in the same respect. Thus whatever is moved must be moved by something, else, etc. This cannot go on to infinity, however, for if it did there would be no first mover and consequently no other movers, because these other movers are such only insofar as they are moved by a first mover. For example, a stick moves only because it is moved by the hand. Thus it is necessary to proceed back to some prime mover which is moved by nothing else, and this is what everyone means by "God." Movement (or action) is caused by something.  Everything action or movement has something that caused the action to begin.  This is the idea that if a boulder rolls down a hill, it didn't move itself, however something caused the boulder to move, and you can, like a detective trace it back to the reason why it was moved.

Unfortunately, you can trace back stuff like this almost infinitely.

  • Boulder rolls down hill
  • Earthquake caused soil to shift
  • Earthquake was caused by heating and shifting of plates
  • When the world formed it was formed in such a way that the plates don't match up.
  • The world was formed by the "big bang" out of nothing?
Aquinas says that it all began with god starting the "big bang" because god was not created.  God just existed and basically has the seeds or cause for his own existence within himself.
 The second way is based on the existence of efficient causality. We see in the world around us that there is an order of efficient causes. Nor is it ever found (in fact it is impossible) that something is its own efficient cause. If it were, it would be prior to itself, which is impossible. Nevertheless, the order of efficient causes cannot proceed to infinity, for in any such order the first is cause of the middle (whether one or many) and the middle of the last. Without the cause, the effect does not follow. Thus, if the first cause did not exist, neither would the middle and last causes in the sequence. If, however, there were an infinite regression of efficient causes, there would be no first efficient cause and therefore no middle causes or final effects, which is obviously not the case. Thus it is necessary to posit some first efficient cause, which everyone calls "God." Same as first argument.  "Infinite regression" just doesn't make sense to the human mind.

Just put in a slightly different way.  When you get to the end of the line, there must be a place that started it all.  It is inconcievable to the human mind that stuff formed out of nothing.

 The third way is based on possibility and necessity. We find that some things can either exist or not exist, for we find them springing up and then disappearing, thus sometimes existing and sometimes not. It is impossible, however, that everything should be such, for what can possibly not exist does not do so at some time. If it is possible for every particular thing not to exist, there must have been a time when nothing at all existed. If this were true, however, then nothing would exist now, for something that does not exist can begin to do so only through something that already exists. If, therefore, there had been a time when nothing existed, then nothing could ever have begun to exist, and thus there would be nothing now, which is clearly false. Therefore all beings cannot be merely possible. There must be one being which is necessary. Any necessary being, however, either has or does not have something else as the cause of its necessity. If the former, then there cannot be an infinite series of such causes, any more than there can be an infinite series of efficient causes, as we have seen. Thus we must to posit the existence of something which is necessary and owes its necessity to no cause outside itself. That is what everyone calls "God." Just put in a slightly different way.  When you get to the end of the line, there must be a place that started it all.  Again t is inconcievable to the human mind (or at least Aquinas's mind)  that stuff formed out of nothing.

It is necessary that something created the universe since you can't make something without raw materials.

 The fourth way is based on the gradations found in things. We find that things are more or less good, true, noble, etc.; yet when we apply terms like "more" and "less" to things we imply that they are closer to or farther from some maximum. For example, a thing is said to be hotter than something else because it comes closer to that which is hottest. Therefore something exists which is truest, greatest, noblest, and consequently most fully in being; for, as Aristotle says, the truest things are most fully in being. That which is considered greatest in any genus is the cause of everything is that genus, just as fire, the hottest thing, is the cause of all hot things, as Aristotle says. Thus there is something which is the cause of being, goodness, and every other perfection in all things, and we call that something "God." Aquinas sort of ranks things. (A little illogical in his ranking system.)

This deals with the idea that for something to be made, something more powerful than it needs to have activated it. 

Cold wood does not ignite on its own.  It needs something hotter than it to start the fire.

hotter = more powerful or excellent
God is more perfect than us = he created us in his image but we're not as perfect.

The fifth way is based on the governance of things. We see that some things lacking cognition, such as natural bodies, work toward an end, as is seen from the fact that they always (or at least usually) act the same way and not accidentally, but by design. Things without knowledge tend toward a goal, however, only if they are guided in that direction by some knowing, understanding being, as is the case with an arrow and archer. Therefore, there is some intelligent being by whom all natural things are ordered to their end, and we call this being "God." Intelligent design (in a way.)

God is the ultimate designer and created the system that makes everything work.

Since the world seems to work in an orderly and predictable way, the world must have been designed by something that was powerful (or excellent enough) to make it work.

God is the divine geometer or divine scientist or divine engineer.

 To the first argument, therefore, it must be said that, as Augustine remarks, "since God is the supreme good he would permit no evil in his works unless he were so omnipotent and good that he could produce good even out of evil." Uses his ranking system to justify the existence of evil.  Saying that evil is a kind of necessity and part of the overall plan.  It is part of the design to bring us up the ranks and realize our own goodness.
 To the second, it must be said that, since nature works according to a determined end through the direction of some superior agent, whatever is done by nature must be traced back to God as its first cause. in the same way, those things which are done intentionally must be traced back to a higher cause which is neither reason nor human will, for these can change and cease to exist and, as we have seen, all such things must be traced back to some first principle which is unchangeable and necessary, as has been shown. Restatement or summary of his thesis.