Visas are not required to gain entry into Chile or Argentina for citizens of most European countries as well as citizens from the United States, Canada, Australia, and New Zealand if you are going to stay for 90 days or less in one calendar year.
Clearing customs is usually a fast process in both directions between Argentina and Chile. Chile does have some prohibitions concerning food. It is forbidden to enter Chile carrying dairy products or any kind of unprocessed food like meat, ham, or salami. Some border posts unload your luggage and fines may be imposed if you infringe on the law.
Every person arriving in Chile will need to complete the arrival card usually handed out on the airplane.
The Patagonia region of Argentina and Chile require no vaccinations to enter the country, except for passengers coming from countries where cholera and yellow fever are endemic. Also, a Hepatitus A vaccination is usually highly recommended for visiting both countries.