What passages support that God once walked the earth as a man? I thought that God once walked on the earth as we do now, but I can't find that in the bible, offhand. 

I thought that Joseph Smith taught that he walked with us and was once a man.  What bible verses did he use to show this?

Where does that teaching come from?
I'm not familiar with Mormon doctrine, so I'm not sure where you're going with your line of questioning, but I'll try to answer the two questions you posed.

Is God Eternal?

The following scriptures describe God as eternal.


  Deuteronomy 33:27 The eternal God is thy refuge, and underneath are
  the everlasting arms: and he shall thrust out the enemy from before
  thee; and shall say, Destroy them.
  
  I Timothy 1:17 Now unto the King eternal, immortal, invisible, the
  only wise God, be honour and glory for ever and ever. Amen.


Did God Walk on the Earth?

In the book of Genesis, God came and walked with Adam in the cool of the day.


  Genesis 3:8 And they heard the voice of the LORD God walking in the
  garden in the cool of the day: and Adam and his wife hid themselves
  from the presence of the LORD God amongst the trees of the garden.


In Exodus God revealed Himself to Moses as a man.


  Exodus 33:22-23 And it shall come to pass, while my glory passeth by,
  that I will put thee in a clift of the rock, and will cover thee with
  my hand while I pass by: And I will take away mine hand, and thou
  shalt see my back parts: but my face shall not be seen.