The usual method is to use the same Gmail, iCloud, Yahoo, or Hotmail account on both devices, and turn Contact syncing on for that account.
Be sure to set up the device with the right contacts first, and make sure you tell it to keep your info (not delete) if it asks.
Before you sync the second device, go to the online version of your chosen service on a computer (that would be icloud.com for iCloud) and make sure the contacts are present.
Then set up your second device, but choose to delete (only deletes the local contacts) if it's offered.
If you need more details, let us know what service you chose. Someone who uses the same provider should be able to walk you through it.