On saying "thank you" in their native language.
The purpose of saying "thank you" is, obviously, to convey gratitude. Language carries with it "emotional force," and each new Azeri word I learn is a bit of an empty shell to me - I have no memories to surround it and fill. Slowly, very slowly, saying "sagh ol" or "sagh olun" or "chox sagh ol" (thanks, thank you (formal) and thank you very much, respectively) has acquired that texture of meaning and feeling that is necessary when I want to thank someone. However, just because the word itself may seem meaningless to me (at first) does not mean that the person on the receiving end is going to feel as though I am being insincere (which is my fear). At one of the pubs in Baku, Shamrocks (which has perhaps the best burgers in Azerbaijan), the waitress ask for my order and I began to give it in Azeri, only to have a perplex look flush across her face. She didn't speak a wink of Azeri, she spoke Russian and enough English. By pointing at the menu all was well and when she brought my order I (somehow) summoned the forethought to udder "spasiba" rather than "sagh olun."
While staying at the Altstadt Hotel, which is a very small, reasonably priced, hotel in the heart of Baku's Icheri Sheher (Old City), I said "sagh olun" to the breakfast staff, who immediately commented on my use of Azeri, as Russian and English are tourist languages in the region. They both expressed great pleasure with hearing Azeri.
Immediately upon arriving at the Moscow Airport, the attendant spoke enough English, though she was noticeably frustrated by my lack of Russian skills and situation of lacking a plane ticket. Upon leaving I said "spasiba" to which she chuckled loudly, and replied (at least I imagine this is what her reply was): "Oh! Now, you speak Russian!"
I also decided that - even though I'm just barely learning Azeri - learning how to express gratitude (assuming that the language has such a phrase) is simple enough. There's little excuse not to give it the ol' college try.
Chinese: shey shey
However, on the flight from Baku to Russia, I accidently slipped out a "sagh olun" to the Russian flight attendant, which ultimately started a lively conversation with the person next to me. He was a Azerbaijani working in Moscow, and was surprise to hear me speak Azeri. Our conversation was mostly basic, but managed to touch on world events and local politics and ended with him handing me his name and phone number and a (typical Azerbaijani) invitation to join him should I ever find myself in Moscow.