Help with refinance process?

Bad Boy

I want to refinance my car to lower the payments and be a little more comfortable but Ive never really been through that process.
I was hoping someone with the experience can kindly offer some details or advice on how to go about it.
For instance, what type of lender would be better? A bank or credit union? Is it possible to try and refinance with the same/current lender?
Is a form of down payment required?
When refinancing, you've made every payment on time but you have average credit score due to other obligations, does credit score still play a great factor?

Thanks for any help.