Go to Settings > My Words > Backup & Sync. You will then receive an email that includes an activation link. Click on the link and Swype will automatically verify your account. You also have the option of manually entering the activation code provided in the email.
Once you have either clicked on the link or entered the activation code, you will be registered on that device. Follow this process for any additional devices you wish to use with the Backup & Sync service. You must use the same email address with each device in order to share a dictionary across devices.