How to add a new iPhone to my list of devices?

Thank you, Raicya. It is actually a simple process as it turns out, but it took me a long time and several tries because the instructions were not clear to me. Also, for some reason the first time I enter my password it is always rejected and I have to go to an "alternate user ID"... But this alternate ID is always exactly the same, but it now accepts my password. And, then when it says on the screen that a passcode has been sent to me, it never shows up anywhere I can find; so then I have to tell it to use a phone number, which does then work. It all gets tiring after going through the whole process several times. I think one problem is it never says very specifically that you have to do the sign-in process on the device which you wish to add to your device list. Once I figured that out it worked just fine. Thanks again for the link.