Determine the origins of the philosophical idea. Find out who first posited the idea and when it was said. Knowing its context can greatly influence the meaning behind the idea.
Read books or find Internet articles about the philosophical idea you want to analyze. Many ideas are subject to perspective, and therefore one idea may have many meanings or interpretations. Find some possible interpretations that you feel might be true.
Break the philosophical idea down into smaller segments, and determine the meaning of the words. For instance, in Rene Descartes' famous quote "I think, therefore I am," the verb "to be" appears (as the word "am.") Determine what it means to "be." This answer may be different for you than it was for Descartes or anyone else.
Determine what the idea means to you and how it's relevant in your life. While you may understand the ostensible definition of the idea, it doesn't have true meaning unless you can find some personal relevance. The easiest way to find relevance behind an idea is to find out its significance in your daily life.
Put your analysis together. After breaking the philosophical idea down, it's time to look at it as a whole piece again. Outline your perspective of the philosophical idea on a sheet of paper. Include the definitions of the words, the context in which it was said and its relevance. Now that you've reassembled the broken-down idea, you can summarize its meaning in a few short sentences.