Hello and welcome to Android Forums. Hopefully I can help you with your problem.
By creating a Google account on your phone and turning on the sync, all of your contacts are automatically saved to your Google account. Those can then be accessed by any device or pc you sign into with your Google information.
Another good thing about using Google is that if you decide to switch devices, those contacts will automatically sync to your new device once you have signed into Google.
There are also apps on Google play that do this too. Google is my recommendation though.
If you have any other questions regarding your device, I invite you to join Android Forums. We have many sections for specific devices which contain a wealth of infor