The General Structure:

I. Name and Year of Case
II. Nature of the Case
III. Facts of the Case
IV. Constitutional Question
V. Decision and Reasons
VI. Concurrences or Dissents

Tips:
1) Do not be distracted by the dicta (rhetoric not related directly to the decision). While it is important to note when analyzing trends, it may confuse your understanding of the case at hand.
2) Use your own language unless the Court's wording is particularly helpful to clarify an argument. The point of briefing is for you to have a handy reference for your own analysis.

EXAMPLE:

Nature of the Case: 1st Amendment, Establishment of Religion Clause

Facts: Engel (and other parents) challenged the practice of a NY public school which initiated daily, voluntary recitation of a non-denominational prayer that was created by the school's principal.

Constitutional Question: Was the NY school's prayer a violation of the 1st Amendment Establishment of Religion Clause?

Decision: Yes. (Black)
-- The prayer was composed by government officials as part of a government program to further religious beliefs. Therefore, it breaches the wall of separation.
-- The fact that the prayer is non-denominational or that observance is voluntary does not free it from the bounds of the Establishment Clause.
-- Pressure for kids to conform is great.
-- Religion is too personal to permit unhallowed perversion by a civil magistrate.

Concurrence: (Douglas)
-- Public officials on the public payroll should not perform a religious exercise in a governmental institution.
-- The same is true for the opening invocation for the Supreme Court and Congress.
-- Voluntary nature of the prayer makes no difference; few would leave during prayer.

Dissent: (Stewart)
-- "Official religion" is not established by letting those who want to say a prayer do so.
-- Court is denying these students the opportunity of sharing in the spiritual heritage of our nation.