Here is very basic vocabulary to get you by in shops. A chart that you can print as a cheat sheet is provided at the bottom of this post.
How much does it cost?/How much is it? = Bu neçəyədir?
Bu = this / neçəyə = how much / dir = it is
How much are the apples? = Alma neçəyədir?
What is this? = Bu nədir?
Language learning materials will give you many phrases for shopping, but you can get by if you understand the shopkeeper when he says "başqa" is asking if you want anything else (literally, another?) and when you want to say that's everything, use "bəsdir" = that's it/that's enough/That'll do. This is pronounced like bəsti, stress on first syllable. You will also hear shopkeepers say "boyurun" to you. This means "Here you go" / "Here you are".
If you want to get fancy, you can say you want something. I want is "istəyirəm", which in Baku is pronounced is-tee-ram. So, "alma is-tee-ram" is "I want some apples". Note that you don't use plural forms for fruit, veg and other products. "I want 6 eggs" is "Altı yumurta is-tee-ram".
It is extremely useful to learn your numbers for shopping, both for amounts and for understanding the price. If you learn nothing but numbers in Azeri, this alone with stand you in good stead. Numbers are quite easy and since you will use these every day - believe me! - you will perfect them with practice in no time. When asking for something, use dənə for piece - "iki dənə" means two of those. For herbs, use dəstə for bunch. So numbers ...
bir = one
iki = two (note that people from outside of Baku may pronounce this "ichi")
üç = three
dörd = four (final d is pronounced more like a t)
beş = five
altı = six
yeddi = seven (second d is pronounced more like a t)
səkkiz = eight
doqquz = nine
on = ten
Now all you need are the tens and you can make any number from one to 100!
20 = iyirmi
30 = otuz
40 = qırx (this looks difficult but just pronounce as grrr and people will understand you)
50 = əlli (make sure this has two syllables, əl-li, not əli)
60 = altmış
70 = yetmiş
80 = səksən
90 = doxsan
100 = yüz
And, of course, you need to know that the money is qəpik for the coin and manat for the bills.
Here is a cheat sheet of the essentials, with common fruits, veg, and other foodstuffs, followed by one for numbers.