I'm not sure where you have been prior to arriving in Uyuni, but if I were in your shoes, I would go by bus and train to the Brazilian border at Corumba, which is in the Southern Pantanal.
Go from Uyuni to Oruro, http://www.travelpod.com/blogs/0/Bolivia/Oruro.htmlhttp://www.boliviacontact.com/en/conozca/oruro.php
then continue by bus via Cochabambahttp://www.travelpod.com/blogs/0/Bolivia/Cochabamba.htmlhttp://www.boliviacontact.com/en/conozca/cochabamba.php
to Santa Cruzhttp://www.travelpod.com/blogs/0/Bolivia/Santa%20cruz.htmlhttp://www.boliviacontact.com/en/conozca/santaCruz.php
From here there is a train, the famous "tren de la muerte" (death train because it goes deathly slow). http://www.ferroviariaoriental.com/http://www.travelpod.com/cgi-bin/keyword2....eyword=Quijarro
Corumba is at the southern end of the Pantanal:http://www.corumba.com.br/
There are plenty of agencies offering trips into the Pantanal from Corumba, but be picky and ask around to make sure you are getting value. Rip-off artists are plentiful.
Starlagurl gave you some good blogs.
Now you have a problem. Keep in mind that before Alaska became a state, Brazil was bigger than the USA. Corumba to Manaus is almost 1,500 miles as the crow flies, equivalent to New York to Denver, Colorado. So obviously you will have to fly. In this case, continue by bus to Campo Grande, where you will be able to get a flight to Manaus, probably via Sao Paulo. If you look at Manaus on the map, you will see it is about half way between Rio de Janeiro and Miami! Here is a good site to find domestic air schedules in South America. Beware, internal flights in Brazil are very expensive. http://www.us.despegar.com/home.asp
Unless you are taking a luxury cruise, travelling by river from Manaus to Belem is by no means the height of comfort. Everything is pretty basic. Many people have said it is really boring because the river is so wide that you really only get to see anything when you stop at riverside towns and villages. It isn't a tour, it's a ferry, so there will be no time for jaunts into the jungle. Plan for a voyage of four or five days. Here is some dated information:http://www.safaribrazil.com/Amazon_River_Ferry_Boats.htmhttp://www.travelpod.com/blogs/0/Brazil/Manaus.html
Now you fly another 1500 miles back to Rio de Janeiro. This is equivalent to flying New York to Denver to Miami.
I am under the impression you should think again about this itinerary.
Rio? Here's what our Travepod adventurers have to say about it.http://www.travelpod.com/cgi-bin/keyword2....d=rio%20janeiro
Mull over this and please get back if you need more specific information.