A lot of different avenues...
There are a lot of back door approaches to a national gun registry. Besides the usual snoopy questions on government forms like Obamacare, there are a variety of ways for the government to track gun owners; these include but are not limited to, gun background checks, records of gun manufacturers regarding parts ordered or guns sent in for repair, handgun carry permits, credit card records for purchases of guns or ammunition, etc. All the government has to do is run your name against all those different records to see if you own a gun, sometimes finding out exactly what gun it is to boot. While there will certainly be times that the government will only have part of the equation, for example, such as a record of purchasing 1000 rounds of 9mm ammunition but no record of purchasing of a gun, that will be enough to let them know that you probably have a gun(s) and probably enough for probable cause if they come a knocking to confiscate it.