how can I extract my contacts from my iTunes backup?

just connect it to your computer and iTunes will pop up and ask you something like, "would you like to treat this as a new phone?"
Answer Yes and iTunes will sync your new iPhone will all the apps, music, contacts, calendars that were on the iPhone4.

It's how people move from one iPhone to another when they upgrade.

P

To extract your contact you need a tool that can help to extract your contacts from iTunes backup file.
I recommend you some tools like:
Wondershare Dr.Fone (a Windows version) or Wondershare Dr.Fone (Mac) (a Mac version).
Not only your iPhone 4S, it also works for the latest iPhone 5, and other iOS

I've used the following guide to be able to poke around where the files are hidden in Windows. Look about 1/3 of the way down the page and try the steps as posted by 'James Knapp'. Don't forget to make a backup file (of the relevant backup files) before you begin.

http://www.makeuseof.com/answers/extract-media-iphone-backup-file-free/

In fact, there are two ways for you to recover your deleted photos from iPhone. First, you can use a third-party tool to directly scan and recover pictures from your iPhone. Second, if you've synced your iPhone with iTunes, you also can regain your deleted pictures by extracting your iTunes backup file.
1. Directly scan and recover contacts from iPhone
a) Make iTunes be automatically sync with iPhone.
b) Enter DFU mode and scan iPhone
c) Preview and recover iPhone contacts

2. Scan and extract iTunes backup to recover iPhone contacts?Link your apple iphone to i-tunes and Back up by choosing Preferences > Back-up from apple itunes, or proper-click on your own iPhone as well as choose support.
a) Scan your iTunes backup for iPhone 3GS
b) Preview and recover iPhone contacts
c) Do backup well

Resources: http://www.istonsoft.com/iphone/how-to-extract-iphone-backup.html

If you are synchronized your contacts with the social networking sites you can recover the lost contacts very easily
You can also get the deleted contact list by extract your back up file
Open itunes on your system
Then plug in your iphone to your system
Then go to the Devices
Then select the iphone unders devices
Now select the option Restore From Backup by right clicking on the iphone device
Then select the option Restore
Now you can see all the contacts were restored on the iphone device

There are two ways to restore your contacts.

video-converter-mac.org/recover-iphone-contacts/

1) Connect your iPhone with computer using bluetooth or USB Cable.


>>Open iTunes

>>Go to "Storage"

>>Click on "Backup and Restore"

>>Wait for a moment.


Your contacts will be restored.


OR


2) Open iCloud.


>>Enter Apple id and password.

>>Go to Storage and Backup.

>>From there Restore your contacts.

>>Close iCloud.

>>Restart iPhone.


You are done.

If you use iTunes as your iPhone manager, you should know there is auto backup generated by iTunes when you sync iPhone with it. Yes, iTunes has done the backup for your iPhone indeed. You only need to restore from the iPhone backup file (SQlitedb file) by iPhone Data Recovery.

Sorry
to hear about your experience. If your iPhone was backed up when the data were on it -- and you still have the backup -- it will be possible to
restore them with an iPhone Backup Extractor - iPhone Data Recovery. Load it up and browse to the
Media/DCIM/100APPLE folder and you should get your data. Here is the steps you can follow:
first, scan the backup file
second, extract backup files of iPhone
third, remember to backup
Hope it can help you. Good luck!