Although I cannot prove it, I suspect the ancient Greeks typically approached philosophy in the spirit of a contest, game, or sport.
One of their core values was areté. The word is usually translated as "virtue" or "excellence", but perhaps a better translation is "being the best you can be" or "reaching your fullest potential".
From what little I know, the Greeks believed the best way to bring out a person's areté was through competition. And, for that and other reasons, I think it's likely they treated philosophy as a competition designed to bring out the best reasoning in the competitors.
Regardless of whether or not I am right about that, it seems that philosophy in their day had only one rule: You could advance any position you wished so long as you supported it with reason(s). Or, in other words, you couldn't simply say, "I think the gods exist" -- you had to state (and defend) your reasons for supposing the gods exist.
Today, it might be the best way to approach philosophy is to think of it as a game you play in order to determine the scope and limits of reason. That is, don't ask, "Do the gods exist", in order to discover whether or not the gods exist. Rather, treat the issue as a case study in the application of reason to the question, "Do the gods exist". After all, if you can learn anything from philosophy it is not whether the gods exist, but the scope and limits of reason in addressing the question of whether the gods exist.
The same can be said of most other well-known philosophical questions. "What is truth?" "What can be known?" "What is moral?" "What is the logic and method(s) of the sciences?" etc. They can all be treated as case studies in the application of reason. The goal is not so much to arrive at a straight-forward answer to each question, but mainly to uncover the scope and limits of reason when applied to each question. And if you come up with a defensible answer, so much the better.
Of course, there are many other ways to approach philosophy. Obviously, one of those is to ignore it altogether. But in that respect, philosophy is also like a sport -- it's not everyone's game.