How to transfer an app from one iPhone to another?

I just got a new iPhone 5c. I want to move only one app from my old iPhone, to my new one. I have already set up my iPhone 5c. I have a 'free music download' that has all my music on my old iPhone. I really want to transfer this app to my new iPhone but I'm not sure how. Is there a way to do this without having to download all my apps from my old phone onto my new one?

If you backed up your old one, you can restore to that back up with your 5C. Which will sync all the apps and settings you had set on your old iPhone to your new one.

Go to itunes on your phone click purchases and download it

As long as the new phone uses the same Apple ID as the old phone, you can install all apps that you've previously purchased for the old phone on the new one, free of charge. If the Apple ID is not the same, there's no way to transfer apps, you have to buy and download them again from the App Store.