First, there's two primary types of 'defenses' based on prior art: anticipation and obviousness (technically there's more, but these two are the most important for this site, a full list is in 35 USC § 102).
Anticipation is the stronger of the two and basically means that a single piece of prior art teaches every element of the claim. That is, the prior art is a mirror image of the claim. Again, there are some minor exceptions for inherent aspects of the claim, but I would never rely on something being "inherent" since attorneys will always argue that it isn't.
Obviousness is the weaker of the two (legally) and means that while not all the elements are in a single piece of prior art, the missing parts are in one or more other piece(s) of prior art. However, the big caveat is that there must be some reason why it would be obvious to combine the pieces of prior art. This area of law is fairly complex and one of the most contentious issues (see KSR v. Teleflex et al). Nearly everyone has a hard time defining what makes something obvious, but the rule of thumb I use (note this is not a real legal test) is that the pieces of art should be related to the same problem and have some sort of relation to each other such that it would not be absurd to combine them.
For issued patents, in terms of the "ideal response," one technique I use for seeing if something is relevant is to try to map all of the key terms (nouns and verbs) of the claim to elements in the prior art. That being said, the ideal response will list the prior art elements for each claim element. In litigation, this is known as an invalidity contention (here's an example, I can't vouch for whether it's strong, but it's the basic format). Basically, an IC in practice is a big table made in Word (I know), that has two columns: the left column has the claim elements and the right column shows where in the prior art is met.
Obviously (no pun intended), this type of analysis is rather time consuming, but I feel an ideal response would at least say: "X is prior art because X shows A, B, and C which corresponds to D, E, and F in the claim." That way, when an examiner looks at the prior art they have a sense of where to start looking in making an argument.
If you are making an obviousness argument, I would do the above for each reference (e.g., X shows A and B, but not C; Y shows C). I would also add language about why it would make sense to combine them.
However, a lot of the requests for prior art involve pending applications. It's important to note that the claims of these available from Google or the PTO's full-text site can and most likely will change significantly as the Examiner finds prior art. In that case, a more general approach is necessary. Instead of a one-to-one mapping, you can just point to prior art and summarize the key aspects that are related to the main inventive concept of the application. Most patent applications have a handful of features (usually 1 or 2) that are the core inventive concept, the rest is mostly known. Focus on those issues and point out why the prior art shows them.
