I don't know what four you'd pick as most common. Here are mine:
- Originalist. This makes sense in that the Constitution is the basis of our system and so it makes sense that we should try to figure out what the people who wrote it meant when they wrote it. Lots of drawbacks: which writers count? Is it the writers, or the people who voted to accept it whose opinions we shold look at? How do we determine those opinions? Do we want to follow them anyway?
All other approaches can be pretty much evaluated in terms opposite to this.
All of these are problematic because they do not stick with what the framers said and, therefore, you can argue that they allow judges (rather than legislatures or "the people") to make law.
But each of them tries in some way to get beyond the problems that I identified with the orignialist approach.
There are many different approaches that judges employ in the interpretation and analysis of the Constitution. It seems to me that the most elemental hinges on if the specific judge belives in judicial restraint or judicial activism. The restraint approach believes that the Constitution is not a document to be taken lightly, or interpreted outside of the words and thoughts present. This approach is rooted in a strict and literalist reading of the document. For these types of judges, the Constitution is not a sword of social change for this is the domain of the legislative and executive branches. Rather, the Constitution is the document that has guided the principles of the nation for 200 plus years and if there is any alteration within it, the structure that has guided the nation is sacrificed. For this approach, if other judges or courts have ruled on an issue, this precedent should be respected and not overturned as these courts have acted within the spirit of the Constitution, dictated by the separation of powers. Two modern historical examples of this approach would be Justices Rehnquist and Scalia. Another approach lies in the approach of judicial activism. This approach calls for judges to broadly interpret the Constitution in light of current events that embroil the nation. These justices believe that the Constitution can be a tool for social change in that it speaks when the legislative and executive process cannot do so as it is the branch of government that does not have to be responsive to the risk of angering the public. The activist judge sees the Constitution as a tool to literally change the nation for the better. Justices Warren and Blackmun are two excellent examples of judicial activism.