Paraguay is a small country and getting around is straightforward once you know the options.
Buses are the backbone of domestic transport. Asuncion's Terminal de Ómnibus is vast and chaotic but functional; virtually every town in the country is reachable from here. Long-distance coaches are good value and often surprisingly comfortable — executive-class buses have reclining seats, air conditioning, and on-board meals. The overnight run to Encarnacion or Ciudad del Este is easy and inexpensive. Into the Gran Chaco, buses run as far as Filadelfia and beyond, but roads deteriorate and journey times increase accordingly.
Taxis are available in Asunción and should be metered; agree a price before getting in elsewhere. Ride-hailing apps (Uber and local alternatives) operate in Asunción and are generally more reliable than hailing a cab on the street.
Car rental is available from the main international companies at Asunción airport. Having your own wheels is the best way to explore the Circuito de Oro, the Jesuit mission ruins near Encarnacion, or the Chaco. Roads between major cities are paved and generally good; secondary roads in rural areas are often dirt and can be impassable after heavy rain. A 4WD is advisable if you plan to venture off the main routes.
Internal flights are limited. For remote areas of the Chaco, small charter planes operate out of Asunción, but scheduled domestic services are minimal. The country is compact enough that buses cover most distances in a reasonable time.
River travel remains an option on the Río Paraguay. A cargo-passenger boat service runs northward from Asunción towards Concepcion and beyond — a slow but atmospheric way to see the country. Hammock space is cheap; journey times are long.