How to email all of my contacts on my iPhone?

I'm about to get a new iPhone because one of the buttons on my current one isn't working. I want the contacts on this phone to go onto the new one but I'm not sure if they are stored on my mac or not through iTunes. Is there a way to email all my contacts or some other way to store them so I can put them on my new phone?

Do a backup using iTunes on the computer. Whether it be on the computer itself or in iCloud. When you get the new one just restore from that backup. All your data would be restored.