Hi, as I couldn't find a good thread with up to date information I decided to create one myself

In this tutorial you'll learn how to backup and restore contacts on Android with fast and simple ways. No PC needed

1. Using Google/Gmail account
When you sing into your Google account on Android it automatically starts to backup all your data on Google and that includes contacts.

You can download Google Contacts app and check all your saved contacts there, you can also easily restore any or all contacts from Google Contacts.

If you can't find your contacts there go to Settings, Accounts, find your Google Account and turn on Sync everything.

2. Backup & restore with an app
If you want to backup your contacts right now and then restore to same device after reset or send it to a friend you can use Easy Contacts Backup application by SimplerApps from Play Store.
It's simple, small and free app and works great, just search for "easy backup contacts".

With that app you can easily backup contacts in .vcf format and restore to any phone(Android, iOS, Java...)

Source: Techdrol

If you faced any problem during any of step above just comment and I'll try to help

You have to enter gmail id on your phone. Go to settings now. Choose accounts option and select the account. Choose option contact and change its sync option. Sync your contacts and you will get your contacts soon.