How to say “Excuse me” in Russian language:

Извините is used for people whom you don’t know. For example if you call somebody in a street to ask how to get somewhere.

Извините, где находится Красная площадь? – Excuse me, where is the Red square?

Простите – the same but it is used more seldom. Which one to use? – It depends on personal speaking style.

Извини is an informal word, used for a person whom you know. Example “Извини, ты уронил шапку! – Excuse me, you dropped your cap!”

And how to apologize?

Извините – I am sorry. Formal. It is used in cases if you for example touched somebody accidentally or stepped on somebody’s foot and so on. “Ой, извините! – Oh I am sorry”

Простите – the same and as it was said before – the difference is only in your personal speaking preference.

Прости is “I am sorry” for the people who you know.

And another meaning of the words “Простите/прости!”

Прости – forgive!

Infinitives of the verbs простите/прости, извините/извини: прощать, извинять