Who made man and woman?

God created them (Genesis ch.1 and 2). With the exception of mankind, we are only told what God made, not how He made it. That fact is in order to stress mankind's importance.

To make man, God fashioned the appropriate shape from dirt and breathed a soul into it (Genesis ch.2). He then made the first woman by fashioning her from a piece of the man's flesh (ibid).

See also:

Is there evidence against Evolution?

Can you show that God exists?

Seeing God's wisdom