I think that the philosophy in the first instance should be learned by engaging with the puzzles that it discusses. It is only after one has got into a sense of the puzzles and how philosophers tackle them that it really makes sense to study the chronology or schools of philosophy. I think this is because at the heart of philosophy is philosophising, doing philosophy rather than studying philosophy. Philosophy is about making sense of ourselves and our situation. To do philosophy is to approach the goal of making sense in a particular way, to engage in a certain kind of practice of enquiry. Philosophical questions aren’t solved by empirical investigation (though that doesn’t mean such investigation is irrelevant), there is a particular emphasis on conceptual clarification, many distinctive marks of philosophizing derive from the enquiries of Socrates, such as an unwillingness to sit with easy or superficial answers, a careful attention to language, the insistent development of a point in both depth and breadth, the giving and challenging of reasons, the uncovering of assumptions, the consideration of counterexamples and implications, and so on.
Philosophy in universities is often described as a “continuing conversation” with the famous dead. (This cannot be exactly right, not least because the cultural significance and context of the views changes.) As in any conversation, we must understand what has been said (history of philosophy) and contribute our thoughts in response. To join a conversation that already exists, to work with the products of an ongoing enquiry, there is much that will need to be learned. And this forms the basis of what university students of philosophy study. But it is central to following the conversation that you understand first what drives it.
So I would recommend a aspiring philosophers start with books that discuss puzzles, rather than books that lay out the development of philosophy through time. I think once you are really into philosophy, and have a good sense of what it is to do philosophy, then the latter kind of book can be very useful. So in the first instance I would recommend, e.g. Stephen Law's The philosophy gym or Julian Baggini's The pig who wants to be eaten. These are more conversational books and so may help with learning how to talk about philosophy with others. Plato's dialogues - and there are many - remain paradigm examples of philosophical discussion; personally, I'd recommend the 'early dialogues' for more balanced conversation in the text, e.g. Crate, Laches, Protagoras, Gorgias. I don't think that there is a special trick to talking philosophy. John Campbell says that philosophy is thinking in slow motion and I agree.