How can you get to Argentina?

You can't drive to Argentina. The Darien Gap in Panama is impassible. Beyond that is Columbia which is very unsafe to drive. Kidnappings and robberies are the norm. You can drive to Panama and have your car or motorcyle to Peru and continue your trip from there. It is as you can imagine expensive. Gas is also leaded in South America and your car/cycle would have to be modfied. So driving and for that matter walking, biking, skateboarding, etc. is out.
You can take a boat to Argentina. There are a couple of options. There are cruise ships that leave the USA and other ports and make stops in Buenos Aires. Not many but there are a few. You presumably would disembark in Argentina. There are tons of great cruises starting in Buenos Aires that go around the bottom of South America and cruise for 10-14 days to Santiago Chile. But I digress. You could book a room on a freighter. Many carry passengers. They are pricey and you eat with the crew but it is an adventure and you will...eventually get there.
So that leaves the obvious...fly by plane. Direct flights are cheapest from Miami. New York and DFW also have a lot of flights. National carriers (Lan, TAM, Avianca, etc. tend to be cheaper but are rarely direct. You usually have to stop in Santiago, Sao Paulo, Bogata, etc. and switch panes). It can add as much as a day to your travels. Aerolineas (Argentine national airlines) and American are you best direct bets.