When using the hermeneutical approach of contextual analysis, What are the main tenets of this approach? How much context is usually necessary to consider?
I'm not sure contextual analysis rises to the the level of an "approach", but it's a tool used by many other schools of hermeneutics—especially those that put significance on understanding what the original author intended to communicate. The basic idea is that when an author makes statement
Take, for instance, Jesus' statement in Luke 14:34a (ESV):
Without context, you could easily interpret that to mean that doctors are wrong to order patients with hyper-tension to reduce their sodium intake. But as you start to look at the statements surrounding this one, that interpretation becomes harder and harder to justify. In fact, Jesus isn't really making any medical advice in this passage at all.
As for what context we need to consider, different hermeneutical schools will have different priorities. Here is my hierarchy of context, which I think coincides well to the Grammatical-Historical approach:
[I could not find a reference to back this up or refute this list. Any suggestions?]
Generally, the higher up the scale and the stronger the affinity, the better evidence a context offers. In the example above, the historical context might suggest that Jesus is talking about a soldier's salary, but the immediate context makes clear the culinary uses of salt are in view. Even so, since an author usually has a choice of several words, they may have multiple and interlocking connotations.
Usually, meaning of a particular statement can be found by examining wider and wider circles of context. We do need to be careful not to impose an inappropriate context on text, however. It's possible that some obscure passages will never be fully understood as we have lost the original contextual framework in which they were written.