Reading philosophy is...different. There are a variety of pieces on the web, many of them handouts for classes like this one, about how to read (and write) philosophy. One I like in particular is at www. princeton.edu/~jimpryor/general/reading.html
I think the key is to see philosophy as a game and regard the papers you are reading not as statements of the Facts of Philosophy (or about a "philosophy") but as plays in defense of a position. In most cases the author will be shadow boxing an imaginary opponent so some of the claims made in the paper will not be made by the author speaking in his own voice, but rather the claims and objections of an imaginary opponent against whom the author is arguing.
Understanding a philosophy paper is like understanding a chess game or a football game. It is a matter of understanding the moves and strategies involved. You should be able to talk about a philosophy paper the way a sports fan talks about an especially interesting game: in terms of offensive and defensive plays, the tactics and the strategies that motivate these moves, and their success or failure to achieve the desired result. To do this effectively, you do need to know some nitty-gritty facts though.
The author’s thesis: Minimally you need to know what he was arguing for--and, as indicated above, this does not mean every detail of his paper, but the conclusion or conclusions of his arguments. For each of the authors we read, if nothing else, you should be able to give a one or two paragraph summary of his position.
Terminology: To understand what is going on you must understand the technical terms that are introduced along the way, e.g. "a priori," "type/token distinction," "definite description," and the deceptively non-technical terms which are given a special sense within philosophical discussions, e.g. "truth," "sense," "reference."
Tools: This is a rag-bag of principles, tactics and strategies that figure in philosophical discussions and facilitate arguments, e.g. Leibniz Law, circularity and begging-the-question objections, the either-it’s-false-or-it’s-trivial strategy, etc. These are standard plays that you learn by reading philosophy. It would be pointless to try to name, list, and memorize these plays but, if you are familiar with them it becomes easier to figure out what an author is doing and also to use them in your own arguments. Again, you pick this up the ability to recognize and make these plays by reading philosophy and asking yourself as you read, what is this guy up to, where is he going and how does this move contribute to his project.
The Standard Arguments and Objections: Have a sketch in mind of the grounds on which the authors’ main theses are supported and the sorts of objections that are put to them. This doesn’t mean memorizing arguments and objections but rather having a general notion of the line of argument that you can, if you think about it, spell out if you need to.