The design argument is perhaps the most intuitive and frequently cited argument for God’s existence. St. Thomas Aquinas states this proof as follows:
“Contrary and discordant things cannot, always or for the most part, be parts of one order except under someone’s government, which enables all and each to tend to a definite end. But in the world we find things of diverse natures come together under one order, and this not rarely or by chance, but always or for the most part. There must therefore be some being by whose providence the world is governed.” 
Here is how we might summarize the argument:
1. Everything that: a) lacks intelligence; and b) acts, always or for the most part, for an end, is guided by some intelligence.2. Nature lacks intelligence and acts for an end.3. Therefore, nature is guided by some intelligence.
Thomas elsewhere supports our first premise by analogy. He states that an arrow (which lacks intelligence) can act for an end (the bullseye) only by the intelligence of the archer.  Some have attempted to dismiss this premise by appealing to natural selection, and the evolutionary process.  The theist need not fret over evolution, however. Granting that human beings have evolved from simpler primates, the evolutionary process itself may very well meet the qualifications of our second premise. This implies that some intelligence has designed evolution to bring about natural selection.
The second premise is easily demonstrable, despite some modern hesitation toward teleology (that things have ends). For instance, there are things in nature that exemplify regularity. Even seemingly chaotic events are intelligible, and since intelligibility presupposes order, it may be inferred that even chaos is ordered in some manner.
It may also be asked, “if nature has a Designer, who designed the Designer?” This question, however, misconstrues the argument. We infer design in things if they meet both qualifications found in (1), but a Designer is an intelligent being, so it wouldn’t be subject to any regress. Further, in order for an explanation to be best, we don’t have to have an explanation of the explanation.  Imagine archaeologists discover ancient pottery in Antarctica, and they infer that this pottery must have been designed. Now, they surely would not have to explain who designed it, or where they came from, etc., in order to conclude that it truly is designed. In fact, if every explanation had to have an explanation, then there would be an infinite regress of explanations, in which case nothing at all would be explained.
It seems, therefore, that the design argument is sound and survives the most common objections.
 St. Thomas Aquinas, Summa Contra Gentiles: Book One: God, translated by Anton C. Pegis, University of Notre Dame Press edition, 1975, ch. 13.35.
 St. Thomas Aquinas, Summa Theologiae, translated by Anton C. Pegis, Random House Inc., 1948, Q. 2, Art. 3.
 Richard Dawkins, The God Delusion, First Mariner Books, 2008 edition, ch. 4.
 William Lane Craig, Reasonable Faith, Crossway Books, Third edition 2008, p. 171.