Quick answer
Повтори́те, пожа́луйста.
patvaríti pazhálusta — plus ме́дленнее — the word that actually solves the problem
The options
Повтори́те, пожа́луйста.Could you repeat that, please.
Ещё раз, пожа́луйста.Once more, please.
Ме́дленнее, пожа́луйста.More slowly, please.
Что вы сказа́ли?What did you say?
Прости́те, я не расслы́шал / расслы́шала.Sorry, I didn’t catch that.
Ask for slower, not just again
Repeating at the same speed rarely helps. Ме́дленнее, пожа́луйста is the request that works, and Russians oblige immediately. Combining both is best: Повтори́те ме́дленнее, пожа́луйста.
The polite -те
Use повтори́те with anyone you address as вы, and повтори́ only with friends. Dropping the -те with a stranger is the single most common politeness slip learners make.
What you hear back
Коне́чно.Of course.
Я сказа́л, что…I said that…
Говорю́: нале́во!I’m saying: to the left!
Typical mistakes
Повтори́ — to a stranger
Повтори́те
The polite form needs -те.
Я не слы́шал — meaning “I didn’t catch it”
Я не расслы́шал.
не слы́шал means you heard nothing at all.
Check yourself
Which do you say to a stranger?
The polite imperative takes -те.