There is a great deal of order exhibited throughout the universe. We often refer to this order as the "uniformity of nature." A simple (not to be confused with simplistic) teleological argument might go like this:
1. Regularity is the result of design. (Premise)
2. The uniformity of nature exhibits regularity. (Premise)
3. Therefore, the uniformity of nature is the result of design. (From 1 and 2)
In other words, whenever something happens over and over again, it is not the result of chance, but of design. Since the laws of nature fit this description, we are justified in concluding that a cosmic designer exists.
The typical objection to this argument is that it leaves the designer unexplained. There are two equally effective responses the theist may appeal to. First, in order for an explanation to be best, we don't have to have an explanation of the explanation. If archaeologists discovered the remains of pottery in a remote part of the world, they would rightly conclude that someone had designed the pottery. This holds true even if the archaeologists have no idea who the person was, where he came from, where he went, etc.
Secondly, theists are happy to admit that the cosmic designer has an explanation. The PSR states that everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. The cosmic designer, far from having no explanation, is explained by a necessity of its own nature. The cosmic designer exists because it cannot possibly fail to exist.
Another way of summarizing the argument is like this:
1. Everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. (Premise, PSR)
2. If the uniformity of nature has an explanation of its existence, that explanation is in a necessary cause. (Premise)
3. The uniformity of nature exists. (Premise)
4. Hence, the uniformity of nature has an explanation of its existence. (From 1 and 3)
5. Therefore, the uniformity of nature is explained by a necessary cause. (From 2 and 4)
Here's the atheist's dilemma. If he says that the uniformity of nature has an external cause, that cause must be supernatural, timeless, changeless and immaterial, in addition to being very powerful and intelligent (per the teleological argument above). Now, this supernatural cause must also have an explanation of its existence, but this can only be found in a necessity of its own nature. After all, a timeless entity is not the kind of thing that can exist and then cease to exist, for that would require temporal becoming.
On the other hand, if the atheist wishes to say that the uniformity of nature exists by a necessity of its own nature, then we still have something very much like God. It's a God-substitute, if you will. It seems that the atheist's insistence that the cosmic designer have an explanation is a sort of backhanded compliment to the theist's defense of the PSR.