A Readly account can be shared on up to five devices. All you will need to do is log in using the same email address and password which you used when creating the account.
If you have created an account with the help of Facebook and want to log on to a device where you're not connected to Facebook, you will need to reset your password. (On help to reset your password click here). When your password is reset you can log in with the same email address that you have for your Facebook account however the new password will need to be entered.