Hrm. I did my exam last year, so I may be slightly off, but:
You study genre because the idea is that all these different types of books fall into different categories. And the reason they fall into one or more of these categories is because they have common elements/themes/similarities.
With crime fiction and relating it to genre and your texts, you might:
-Take one of the main conventions> Private Investigator
-Pick out, in your chosen texts> The main character and how they are similar to, or different from the convention of the "Private Investigator".
For example I might be doing K.C. Constatine's "Cranks and Shadows", and "The Skull Beneath the Skin".
>I'll start with the crime fiction genre convention of the Private Investigator. I'll point out the standard idea of the wise-cracking, hard-drinking, lonely, poor PI who generally started the genre, before I move on to point out the fact that in "CaS" the convention has moved with the times, and I'm now given a Police Detective, rather than a PI. And then I might point out the fact that although Cordelia (that was her name... right?) in "SBtS" is a PI, she too is a product of the genre conventions changing with time - she's a chick, she doesn't drink to excess etc.
... I hope I'm not confusing you.
It's just about picking out how your texts have taken the conventions, and either used them as they are, or used them in new and interesting ways.
I think.