How to Sync Your Android Contacts to New Devices

1. Export contacts from old phone. - 
First, export the contacts from your old phone into a vCard or CSV file.

2. Import contacts to Gmail account.
Open up your Gmail account and import the contacts from your phone to your account online.

If you don't have a Gmail account (and with Android, everything is just much easier with a Google account), go to step four.

3. Import contacts from Gmail account onto new phone.
Set up your Google account on your new phone/tablet and your Gmail contacts will automatically populate and sync with your phone contacts.

4. Import contacts from file onto new phone.
If you don't have a Gmail account, connect your new phone to a laptop or desktop and transfer the vCard or CSV file from your old phone onto your new one.

Then, import the file from your phone's storage.