Another note that might help, in addition to what Aloïse wrote: if you're asking about the number (countable) of a thing, you need to use the plural, so you would write "Combien de genres." The singular is for when you are asking about a non-countable quantity, as in:
"Combien d'acide sulfurique faut-il boire par jour ?"
"Combien d'or avez-vous donné aux extraterrestres qui ont atterri dans votre jardin ?"
A coffee shop is "un café."
To make it a complete sentence, you could use the "y a-t-il" construction: "Combien de genres de café y a-t-il au café ?" = How many types of coffee *are there* at the coffee shop?
I'll leave it to an expert to tell you whether the best word to use here is "genre," "variété," "préparation," or something else. And how to make that sentence less repetitive. :-)