To put a spin on something means to twist or turn the truth, either slightly or more. There's a negative aspect attached to twisting and turning the truth, so adding 'positive' to that idiom gives you, put a positive spin in it, or make sure the result of the spin (the untruth) is positive. For example,
Max: Pat has to go to the dentist today.
Sam: Is Pat scared?
Max: Yes, so I'm not going to say anything.
Sam: Put a positive spin on it. I know that dentist. She doesn't use needles. She uses gas, and she lets you watch MTV while she is working on you.
Truth: The dentist can be a painful and scary experience.
Positive Spin: There're pain management techniques.