Does god speak? Yes, of course. All prophets in the Bible heard the voice of God and wrote it down so that that we can read it.
How was it recorded? Simple, by writing it down. In some cases like the creation account in Genesis where no one was there to listen, God might have told to Moses what happened and Moses recorded it.
Does God have a mouth? Well, that's a tough one to answer since we don't have all information about God. We don't even know if God has a form or not. It is not necessary that God should have a mouth. For instance, an electronic loudspeaker can produce sound without having a mouth. If human can produce sound electronically, I believe that God has countless ways of producing sound and a better quality than what we can produce. What can you expect from those Bible authors who have never seen the electronic sound system? All they heard was a voice and they recorded it.
Jesus Christ is the Word of God
In the beginning was the Word, and the Word was with God, and the Word
was God. He was with God in the beginning. Through him all things
were made; without him nothing was made that has been made. (John
In the beginning God created the heavens and the earth. Now the earth
was formless and empty, darkness was over the surface of the deep, and
the Spirit of God was hovering over the waters. And God said, “Let
there be light,” and there was light. (Genesis 1:1-3, NIV)
Some theologians would say that all the three persons of the Trinity were involved in the creation process. First, the Holy Spirit was present on the site where the creation work was to be executed. Second, God the Father gave the command. Third, the Word(the Son) came out from the Father and complete the work of creation. This would imply that when God said “Let there be light”, Jesus Christ the Word of God came out from God and executes the command just as a computer would execute computer programs. Jesus would be the program, God would be the computer and the Holy Spirit would be the electricity which provides the power required to make the whole system working. Just an analogy. :)