I wrote a quick travel guide type thing from my trip to Paraguay in 2005...

Apparently there is a really bad outbreak of Yellow Fever at the moment in Paraguay so get immunised well before you get there if you are inspired by this!!!

There are several boats a week that travel along the Rio Paraguay, a long and sultry river which begins in the Pantanal of Brasil and ends at the border with Argentina in the south. The passenger boat called the Aquidaban seems best avoided because of the crowds but the weekly journey of the Guarani, a freighter is a real treat. I say treat as it is far from comfortable or reliable but if you want an authentic, no frills view of life on the river then this is it.

The majority of the boat is taken up with all kinds of goods for the small towns and villages along the river. Food, furniture, oil, motorcycles and a huge load of gravel we collected en-route were part of the cargo. For a negotiated price of about $20 we secured a rough dark cabin above the engine.

There are no real comforts but food can be taken with the crew and the few locals who take the boat between villages. Sitting up on the tin roof watching the river go by and observing the comings and goings as the boat gets caught on sandbanks, loads and unloads and the crew get on with the tasks of running the boat. Fishing off the back of the boat in their spare time to have the old lady cook up the catch in the evening.
The passage takes roughly 2 to 3 days depending on all of the above. It is a working freighter so as such the passengers are the last concern of the crew but having said that we never felt unwelcome or in the way.
Small towns such as Puerto Pinasco and Puerto Vallemi slowly pass by. There is a huge chest freezer with beers in to help pass the time and a really ancient looking giant tv showing a constant stream of Football and Paraguayan soap operas by the kitchen area at the back of the boat. The toilet and the shower are one in the same being just a hole in the floor to stand over and a shower head directly above it, saves time i guess. All very basic and in no way designed for tourists expecting comfort or service. Brilliant. Take a good book and let the river slowly pass by.

The weather went from sweltering airless heat to heavy rain and strong wind so be warned.
The end of our ride came after 3 days at Isla Margerita which is at the border with Brasil, we arrived at midnight and with Brasil on the far bank of the river we quickly found some cheap lodging right next to where we had disembarked. The owner of the room also happened to own a boat so for a small fee took us across the river the next day. We had arrived in Brasil.
None of the towns have a real port or dock so the boat just ties up on the riverbank. Concepcion is a major town by Paraguayan standards and can easily be reached by bus from Asunción. Find the river and the Guarani leaves sometime on a Tuesday. Speak with the captain to negotiate your passage. Timings and days vary so prepare to be very patient.