The USA has land attached to how many continents?

Geographically speaking - four. North America, South America, Asia, and Australia. Most of the US is on North America. Puerto Rico, Navassa, and the US Virgin Islands are officially a part of North America but geographically closer to South America. The eastern most islands of Alaska are closer to Asia as is Wake Island and most of the Northern Marianas. Howland, Baker, Guam, American Samoa and a wee portion of the southern Northern Marianas are closest to the Australian mainland. You can also add Antarctica but that is unofficial - but no doubt the USA will one day lay claim to parts. The USA has no part within a geographic reach of Europe nor Africa.