When you buy a new phone, a support CD is supplied with the package. On that CD there is software which allows you to manage everything related to your phone (if it supports it!) like: contacts backup/transfer, content, messages, images, video files, etc.
If it's a smartphone then you can use the following applications to transfer contacts, based on the operating system:
- Android: Samsung Kies is the support software for Android based phones and Samsung phones
- iOS : iTunes allows you to perform these operations.
- General : Wondershare MobileGo can be used for both Android and iOS devices.
Upon installing these application, you will have tutorials or wizard guides showing how to transfer contacts. Have no worry because the process is extremely simple.