* 何月生まれですか? (Nan-gatsu umare desu ka?) This is a polite and common way to ask. It literally translates to "What month's birth is it?"
* 何月生まれ? (Nan-gatsu umare?) This is a less formal version, suitable for friends or family. The question mark is implied in the intonation.
* 生まれたのは何月ですか? (Umareta no wa nan-gatsu desu ka?) This is a more formal and slightly longer way to ask, meaning "What month were you born?"
Remember to use the appropriate polite ending (です - desu) when speaking to someone you don't know well or are of a higher social standing. You can omit the です in informal settings.