how to do proper keyword research?

[Jeff]

I understand the theory of keyword research perfectly but I do not know how to put it into practice.

How do I optimize the article titles?

If i wanted to write an article like "Keyword Research: How to optimize article titles," would you research the entire string or each of its parts?

How would you finally decide what to use?

How do you then optimize the content to include High traffic and low competition keywords?

Is there any good tool to use to do this? For some reason the google adwords tool doesn't make much sense to me and it seems more targeted towards paid advertising than organic searching