I’ll explain how I approach a philosophical text, then list some books you can read to refine your approach further.
The main thing when reading a philosophical text is to read actively – take notes, write in the margins, anything so that you’re not just letting the words pass over you. In addition, you need to read any philosophical text that you want to understand and remember a minimum of two times.
The first time you read a philosophical text, you need to put aside your personal views and just try to understand what the text is saying. Don’t evaluate the argument at this point, or your evaluation will distort your understanding of the content of the argument. Be able to prove that the philosopher is actually asserting each component of the argument you think he is making with specific passages in the text.
Once you understand the argument of the text, you can read it again to evaluate the argument. It helps many people to make an “argument map” or lay out the argument of the text in front of them as a syllogism so that the premises and inferences are clearly displayed.
If you read a philosophical text carefully, take notes, evaluate it thoughtfully, and write an essay explaining your point of view, there is a good chance you will remember it for the rest of your life.
One book that was recommended to me by a very good professor when I was a college freshman is The Practice of Philosophy by Jay F. Rosenberg. Rosenberg focuses on how philosophical worldviews get articulated and defended in the dialectical process of formulating and criticizing arguments, and he presents some common ways in which philosophical arguments are criticized.
Lewis Vaughn’s book Writing Philosophy is good, as well. It has two chapters that cover how to properly read a philosophical text, and it covers how to formulate and criticize a philosophical argument.
If you want a text that covers some basic issues along with readings, you might try Core Questions in Philosophy by Elliot Sober. Sober presents classic philosophical arguments clearly and explains how a philosopher could go about criticizing them. There is also a section near the beginning that explains inductive and deductive arguments.