It may be helpful to compare/contrast it with another software development methodology. Agile Methodology is centered around organizing teams from veritable backgrounds together to complete a project. Other methodologies may be focused on ... [fill in the blank]
You said you already have the pros and cons laid out, so you just need some situations where you can decide what method you would use. You may also use several methodologies within the same project.
As small team of Java coders may be using one method to organize themselves, while another team may use a methodology that fits their paradigm. A business team may be sponsoring the project, for example, but they might use another methodology. When the two (and other teams) come together, they may govern their interaction with yet another methodology!!
I hope this helps.
Good Luck