You can use a cloud system Apple - iCloud. Register your phone to iCloud. To do this, go to menu "Settings" phone (the app looks like a few grey gears and features to the desktop by default). Select the Basic tab, the item "software Update". Update your iOS to the latest available version.
After upgrading iOS system will automatically prompt you to connect to iCloud. You will need to register a mailbox, select the user name and password. Then navigate back to "Settings". In the Main tab you will see the iCloud panel. Put the slider next to "Contacts" in the true state (pressed to the right edge).
Now all your contacts from the phonebook are synchronized with the cloud storage iCloud. On the website icloud.com you can copy them to a spreadsheet or text file. In addition, you will be able to store in "Apple" the cloud confidential information and the photos on the phone.
The standard way of copying contacts from iPhone - using app sync Apple devices to iTunes. Download it on the official website of the company.
Install iTunes. Click "File" in the task pane, select "Sync device". Choose from among the synchronization objects "Contacts-write". Information telephone and address books will be stored on your computer in iTunes-Backup.
You can also use the services of your service provider. Major operators (MTS, Beeline, MegaFon, Tele2) offer a service "Second memory". You can store numbers to your phone book on the server of the operator. Although a paid service, it solves the problem when changing the machine, and if I lose my phone.
The company "Yandex" offers a convenient service to change the phone - "Moving". You must select the type of the old system (Apple iOS), the type of the new, connect the phone to the computer. The system will automatically connect to your phone book and copy the contacts that are automatically transferred when you change your phone.