how would you explain the evolution of an organism such as the eye, which does not function if one part is missing?
Actually, Darwin himself thought up a scenario that explains how the eye may have evolved.
This link explains a bit how the eye may have evolved. It is nice because it provides a direct link to Darwin's
Origin of the Species, right where he first gives his scenario.
The important thing about irreducible complexity is that systems that are irreducibly complex may still have evolved from simpler systems; here is a link to
talkdesign which has some resources refuting the intelligent design movement. Here is a link to
an article about the evolution of blood clotting.
The second point is that the eye is not even irreducibly complex to begin with; for example, the lens is unnecessary - the nautilus has a simple eye without a lens - the pin hole camera principle works just fine. See the first link above.