My friend has an elf that has "Tap: Untap a forest." can he pay something that has a cost of 3 forests by tapping 2 forests tapping the elf then tapping the just untap forest?
As long as its in the same phase, yes.
You tap land for mana. This untaps a land for you and you can tap it again adding another mana to your pool.
Your mana pool empties after each phase, but as long as you are "floating" (tapping and not using) the mana in the same phase, you can create and add and use as much as you want, but once you verbally initiate the next phase, (I.E. Lets say it is Main Phase 1, you initiate your Combat Phase, during your 1st Main Phase you had 2 mana still in your pool, once you initiate the Combat Phase, your 2 mana gets removed from the pool, or "emptied") your pool is emptied. So to make a long story short, yes, he can do that with his elf. I'm guessing it's {Arbor Elf} that is doing this? =P
Also, it's good to get well acquainted with the Turn Order, this is one of the best pictures I could find. http://www.donsmagicandsundry.com/catalog/M10_Rules_Tips_3.jpg
Yes, as it's been said. He can't do this during the casting of a spell because untapping the forest is not a mana ability. Mana abilities are unique because you can activate and resolve them during the payment of the cost of a spell or ability.