So, what does God say about birth control?
Well, it very simple actually; God says in the bible that children are a blessing-
Psalm 127:3-5 Sons are a heritage from the LORD, children a reward from him. Like arrows in the hands of a warrior are sons born in one’s youth. Blessed is the man whose quiver is full of them. They will not be put to shame when they contend with their enemies in the gate.
That means we shouldn't reject a good thing that the Lord bestows unto us or say no to it.
If we were to win the lottery and we were to receive it by means of payments each month, we wouldn't say "Oh I have had enough now, no thank you, that's enough". 

So, in answer to the question, "What does God say about birth control"?, he doesn't!

It's plain that God doesn't want us to reject what he gives us; he clearly states that it's a gift and a blessing!