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Here are the points which make up Dawkins' central argument (taken verbatim from God Delusion, my comments in orange):

1. One of the greatest challenges to the human intellect... has been to explain how the complex, improbable appearance of design in the universe arises.- Agreed


2. The natural temptation is to attribute the appearance of design to actual design itself. - Agreed


3. The temptation is a false one, because the designer hypothesis immediately raises the larger problem of who designed the designer....It is no solution to postulate something even more improbably. We need a "crane", not a "skyhook", for only a crane can do the business of working up gradually & plausibly from simplicity to otherwise improbable complexity. - This is where I disagree. To me, it makes more sense that an eternal God is a less improbable and easier explanation than something from nothing.


4. The most ingenious & powerful crane so far discovered is Darwinian evolution by natural selection... - Agreed


5. We don't yet have an equivalent crane for physics. Some kind of multiverse theory could in principle do for physics the same explanatory work as Darwinism does for biology. This kind of explanation is superficially less satisfying than the biological version of Darwinism, because it makes heavier demands on luck. But the anthropic principle entitles us to postulate far more luck than our limited human intuition is comfortable with. - Agreed


6. We should not give up hope of a better crane arising in physics, something as powerful as Darwinism is for biology. But even in the absence of a strongly satisfying crane to match the biological one, the relatively weak cranes we have at present are, when abetted by the anthropic principle, self-evidently better than the self-defeating skyhook hypothesis of an intelligent designer. - Agreed, somewhat.

(Dawkins, The God Delusion, 2006, pp 157-158)