Any advide on transfering iphone contacts to itunes?

[youtuy]

So here's the thing, I accidently spilled water on my iphone 4, although it has been fixed, it still get kind of "unstable
", sometimes it just suddenly shut itself down.
Now I'm saving money for the new iphone 5, but I have a pile of important contacts saved on my watered iphone 4 and I'm so afraid that they'll be gone with the damaged phone right before I could get a new one. But if I can copy these contacts to itunes, then next time I'll be able to transfer them to the new iphone,right? Or just copy to computer? Any difference?
Anyway, I just want the contacts to be backuped, any good idea? I don't mind if I have to pay for something but it would be the best if there's a free and easy way.Help me please.

[jamsen]

You can sync contacts, calendars, bookmarks, and notes with other applications on your computer. This allows you keep all your information in sync across multiple computers and iOS devices. The settings for these items are all in the Info tab for your iOS device in iTunes. With your iOS device connected to the computer, select your iOS device. Then click the Info tab.

To sync contacts with your computer, choose "Sync Contacts with" within iTunes for Windows, or "Sync Address Book Contacts" on your Mac.