Deidara uses the mouths in his palms to prepare clay for his explosion release. How did he get these mouths? Was he born with them or did he acquire them some other way?
Somewhat contrary to the other two answers, it is actually unknown how Deidara got the mouths in his hands, as it is not revealed in canon.
The Wikia does mention the hands in their Iwagakure Kinjutsu article, however it's important to note that the part talking about the hands is merely speculative.
Quote from Wikia (emphasis my own):
In this Data Book article, it mentions the technique that he steals from Iwagakure is the ability to fold his chakra into clay. It can be guessed at that this is where the hands come from, but it's possible that he got the hands elsewhere and can merely use that ability through those mouths.
The first thing to say is that he was not simply born with them, after he lost both arms fighting gaara and then naruto and kakashi, he had replacement arms grafted on and the donor arms also had the mouths. Naruto wikia has this to say on the subject: