Aerolíneas Argentinas flies daily to Buenos Aires.
Buses to Encarnación (AR$35, every 20 minutes), Paraguay, stop at the corner of San Lorenzo and Entre Ríos. With queues and border formalities, the trip can take more than an hour.
Everyone gets out to clear Argentine emigration. If the bus leaves without you, keep your ticket and catch the next one. The same happens on the Paraguayan side. There are fairly honest moneychangers hanging out by Paraguayan immigration. Get small denominations: a 100,000 guaraní note is hell to change.
Buses from Posadas
Paso de los Libres
A shiny modern rail service connects Posadas and Encarnación in Paraguay, leaving Posadas every 30 minutes from 7:15am to 6:15pm (AR$35, eight minutes). You clear both Argentine and Paraguayan authorities at the Apeadero Posadas station.