Microsoft outlines Here their various syncing options. It willl depend upon the computer you have will depend upon the sync features. I will tell you if you have a Windows 8 PC, the sync is native.
Also, if you have a Microsoft Account set up on the phone, your contacts automatically back up to that account. You can visit live.com or outlook.com to login and see these contacts. These will also automatically download onto any new Windows Phone once you log in.
Hope this helps!
*I am an AT&T employee and the postings on this site are my own and don't necessarily represent AT&T's position, strategies or opinions.
Your contacts are not really stored on the phone, they're just synced there. They would be in your hotmail account and/or your google account and/or your exchange account on the web/cloud/whatever you want to call it.
It would be far easier to download/sync them from those web sites.