You would typically use such a correction after you found a significant effect of some independent variable with several levels (categories) upon some dependent variable (usually a continuous measure). After that you could run e.g. a pairwise comparison test which compares all possible pairs of the independen variable. Since you then use the same data to run several test on these, you need to correct for this 'multiplication' of tests. The best known is the Bonferroni correction. But, there are several less conservative tests, see e.g. Article What is the proper way to apply multiple comparison test?

I am not familiar with the article Jos Feys referred you to. I'll have to take a look at it. Meanwhile, these two 2005 Lancet articles by Schulz & Grimes are among the most thoughtful pieces I've ever seen on the so-called multiplicity problem. HTH.

Article Schulz K, Grimes DMultiplicity in randomised trials I: endpo...

Article Multiplicity in randomised trials II: Subgroup and interim analyses

1. Probably never. In statistical terms, Holm's dominates it. So in situations where you might use Bonferonni's, think about using Holm's. But there are others which may be applicable for your situation, so if you want to know about a specific method please provide more details.

2. Changing your question of when to adjust, when you have a set of hypotheses and want to control the familywise alpha for saying an effect is sig. It can be used for any family of tests (so the tough question is what constitutes a family). You'd include all the p-values in that family. In many situations you should be looking for patterns of relationships, rather than if any single hypothesis is sig.