Now here’s a topic that’s so basic I can’t believe I haven’t done it yet.
If you know how to say “thank you” in Arabic then you’ll recognize the Turkish phrase teşekkür ederim, from the Arabic tashakkur for “thanks” combined with the Turkish helper verb etmek to mean “to thank,” then conjugated into simple present first person singular. You could skip the verb altogether and just say teşekkürler (“thanks”), and adding the Turkish word çok (“very”) to either (çok teşekkürler, for example) makes “thanks a lot.” A more Turkish way to say thanks is sağol (or sağolun for talking to a group or more formally), which literally is a command to “be well” but idiomatically means “thanks” or “cheers.”
There are many options in terms of a response: estağfurullah comes from an Arabic phrase begging God’s forgiveness, but here it means something like “don’t mention it”; rica ederim (from rica etmek) means to ask or make a request, but like the Persian khwahish mi konam it has an idiomatic meaning in this situation; buyrun literally means something like “here you are” but is often used here; and (my favorite) bir şey değil literally means “it’s nothing.”