The best source for the nature of the Godhead when speaking with non member friends is the New Testament. The New Testament is chalked full of clear examples of the nature of the Godhead three beings units in purpose.  
 
A great chapter to refer to is Colossians chapter 1, verse 3 states that God is the Father of Jesus Christ (so there is at least two distinct beings) verse 15 states that Christ is the Firstborn of all creatures (so once again reinforcing his role as the firstborn spirit child of Heavenly Father and there being two distinct beings not one) 
 
The most likely verse anyone will quote in defense of the trinity is John 1:1, "In the beginning was the Word (Christ), and the Word, was with God, and the Word was God."  
 
I always point out here that while the english translation can make it look like John is saying that Christ is Heavenly Father (if you ignore the middle part of the Word being WITH God (hard to be with yourself I think! ) that the original greek makes it much more clearer that Christ is not the Father but a member of the Godhead. A more grammatically correct translation is the Word was a God, or the word was divine.  
 
Remember in the end though that any discussion about your faith must not have the Spirit of Contention present, bearing testimony and not having a argumentative spirit is the best way to show the love of Christ when facing questions of our doctrine,  
 
In the end the true testimony comes from the Holy Ghost not any theological discussion.