Border crossing from Chile into Argentina normally is quite easy as tourist visas of 90 days are granted to many countries in the world, but it can (and normally does) take some time because no-one is in a rush in Latinoamérica, the border patrol stuff is not an exception. Especially if you take a bus ride at night waiting hours at the borders are between 3-5 hours, during the day 1-2 hours.
Taking a bus from Santiago de Chile to Mendoza (Argentina) is a nice ride through the mountains. The bus costs about 25.000 CLP (39,00 USD). Included in the price is a comfortable seat, a sandwich, a glass of water and impressive views into the dry mountains in Chile and later the lesser dry mountains in Argentina.
(Landscape of the mountains of Chile)
(Landscape of the Argentinian side)
As everywhere in Latinoamérica, special attention to the luggage should be paid at the bus station in Santiago de Chile. It is a crowded place with people from all over the continent. My big backpack for example got stolen there, without possibilities of recovery.
Additionally, to exit Chile it might be necessary to show the “Tarjeta Unica Migratoria” of the Departamento de Extranjería y Migración, that one receives when entering the country of Chile. It looks like a supermarket recipe. I personally did not have to show it as we did not even stop at the border of Chile, but I heard of cases where they asked for it.