I'm currently studying philosophy at the local university, so here is my advice:
As far as I'm concerned, philosophy is all about arguments. What I'm doing as a student is trying to do the following:
-Learn to understand the types of reasoning philosophers use, which is mostly deductive logic. Once you master the basic rules of logic, like (basic propositional and predicate logic) then its on to the more advanced topics (like modal logic).
-Understand the terminology and distinctions that philosophers use. Here are a couple distinctions any student should know:
-a priori/a posteriori
-Understand as much the history of philosophy and understand contemporary philosophy as well. In general, anybody who sincerely wants to become a philosopher must read a variety of material and not limit himself to only a few books. Also, please do not kowtow to any philosopher no matter how popular or influencial. To kowtow means to literally bow your head, usually in a worshipful manner and thats not how you should view any philosopher. One mistake I see alot of people do is uncritically accept whatever a certain philosopher has to say just because they like what that particular philosopher has said. From what I've observed, some of the most kowtowed philosophers include Aristotle, Thomas Aquinas, Friedrich Nietzsche, and Ayn Rand. There are certain people who will accept whatever their intellectual god has to say and ignore any criticism made by other philosophers.
Of course you'll find some philosopher that you'll agree with more than others. I was introduced to philosophy by reading the work of Roderick Chisholm (1916-1999), particularly the first edition of his Theory of Knowledge. As much I respect and admire his work, I must also read his work critically and understand the objections made to some of his ideas. I know it is unlikely that I will agree with him on every issue. Here's a short list of contemporary philosophers people should know more about, since most people have not heard of them and have made important contributions (in no particular order):
-Willard van Orman Quine
-William G. Lycan
Of course but there are many, many more. So keep reading!
-Probabily the most important virtue I have learned is patience. Philosophy takes time to understand. Sure, there are many different positions that can be taken for an issue and philosopher rarely ever agree. But all that means is that the questions are hard to answer, so don't get overwhelmed by it and please do not jump to conclusions on a subject.
Well, I've only discussed a little bit about it and I haven't done much justice to the task of discussing it, but I hope this is of some help. Good Luck!