Q: how do i transfer contacts from my old iphone to my new one

Everything should be on your computer.

You should be syncing to your comptuer regularly, importing pics regularly and transferring purchases regularly.

Just sync the new iphone to your computer.

iOS: Transferring information from your current iPhone, iPad, or iPod ...

restore the latest backup of the old phone to the new one.

for contacts only if you dont want to use backup I use the app MCBackup.
Go through this article on Product's Support which shows you how to transfer from iphone to iphone 5C step by step:
http://www.flash-video-soft.com/blog/?p=1322