If the Big uns and Crooked Teef Goblins are in the battle field area and both are undamaged. The Ork player attacks the other players Battle field area that has one possible defender in it. The defending player defends with the unit and it does one power in damage to one of the attackers. He assigns it to the Big uns does toughness kick in and prevent that one damage. Also if the defending player assigns the one damage to the crooked teef goblins will toughness kick in and prevent the damage or not? The rules do not even come close to explaining this. Do burned areas still provide resources and cards? Thanks a Ton in advance for answers!
This seems like a very simple question with a very simple answer, so I apologise if I am mis-reading it.
Big-uns have tougness 1 ONLY when a damaged unit is present anywhere on their battlefield.
In your scenario neither of your units are damaged, so neither unit has tougness.
They attack and the defending unit assings 1 damage to the big uns (who still currently have no tougness as they are still not damaged.
The damage is then actaully dealt (so the big uns take 1 damage) and now both the big uns and the crooked teef goblins have toughness.
Notice that it is impossible for the big uns to receive the tougness before the damage is actually dealt, and impossible to deal the damage after giving them toughness (unless the orcs receive damage from elsewhere before damage is resolved).
I would suggest re-reading the section on assigning and dealing damage and the necessary steps required to do that.
Hope it helps