How to say "here you go" when giving a gift?
When you are handing over a gift: 


送给你。("A gift for you."), or 
给你。 ("For you."), or 
这是给你的。("This is for you.")


You can expand it, like:


这是给你的...。 ("This is a/some ... for you."), or
这本书是送给你的。("This book is a gift for you.")


Don't forget that in some cases, you have to use 您 instead of 你.

You can make it more polite by saying: 请收下 ("Please accept it.") or if you are accepting a gift and your partner makes some polite comment about the gift and/or the occasion you can say: "谢谢，我收下了。" ("Thank you, I accept it.")