Correct way of saying "Again please"?

Can you tell me the correct way to say this? If I wanted to ask someone to repeat what they said by just saying "Again please", would I use "Ponownie" or "Jeszcze raz"?

Thanks

Proszę powtórzyć = Please repeat. Jeszcze raz more rarely and only if you know the person well.

"Proszę powtórzyć" is rather a formal phrase, followed by more polite-sounding "Mógłby Pan powtórzyć? / Mogłaby Pani powtórzyć?".

When talking to friends or close family (of similar age or younger), it's perfectly normal to ask "Jeszcze raz?" or just to say "Powtórz. / Powtórz proszę."

The most common I use and hear are variations of "Możesz powtórzyć?"

Also common is "Słucham?"

I would use "słucham" mostly in a situation where the other person tells something which you find hard to believe or doubt...and then only with a person you know well

Actually, I'd say quite the opposite. It does not necessarily communicate disbelief at all, though in some situations, it can, depending on context and tone of voice. And it's acceptable even in the most formal situations. I don't find it relaxed or informal at all. In the informal situation you depict, I would be more likely to say "Wątpię.","To chyba jakiś żart?", "Żartujesz!", "Daj już spokój!", "Co ty bredzisz?", or even "Ale pierdoły.", depending on how strong I want to express it.

Youre exactly right - the tone of voice has a lot to do with it. As in "Co Ty gadasz?", just "co Ty?" or even "pojebało Cię?"