Over and over, Plato tells us that the method which the philosopher uses to reach this science is dialectic. Despite his frequent discussions of dialectic, however, scholars have remained divided about just what dialectic is. It's a dreadful neologism and for all I know there may be a perfectly acceptable, useful one already available. There seem to be at least as many philosophobic people as there are people who think they can't do mathematics or operate a personal computer. In reality, operating a PC is, as you would already know, simple.
Basic math is part of daily life.
No one expects you to become another Socrates. Piecemeal To impress others or satisfy curiosity, you don't need a structured approach. To do this, you could just read bits here and there. Chances are he knows only select quotes, pithy one-liners and speeches, rather than entire plays and dialogues. You can, too.