Thank you and sorry (dziękuję, przepraszam)

Thanking

dziękuję is thank you — it is the 1st-person form of a verb, so it literally means I thank. dzięki is the short informal version, like English thanks.

The reply is nie ma za co — don't mention it, literally there is nothing for which.

Please, and here you are

proszę is the workhorse. It means please, but also here you are when you hand something over, and go ahead when you let someone speak. proszę bardzo is its emphatic form, and doubles as a second way to answer thank you.

Apologising

przepraszam covers both sorry and excuse me — an apology and a way to get someone's attention. The reply is nic nie szkodzi, no harm done.

okej and w porządku both mean OK / all right; the second is the more Polish of the two.