How do you register a gifted rifle?

If you're in the US, there isn't going to be any requirement to register a rifle. The only times rifles have to be registered is when they're Title II NFA regulated items (rifles with a barrel under 16", full auto rifles, etc.). The one exception to this rule is California, which requires registration of all so-called "civilian assault rifles" and .50 calibre rifles - neither of which can be gifted or transferred any other way to anyone within the state of California.