The best way to buy tickets to Rio de Janeiro is to use a consolidator. Consolidators usually specialize in a geographical area and buy tickets from the airline at a bulk price. In turn the consolidator sells the tickets to you at a cheaper price than the airline.
These are some of the best sites out there. If possible do try to buy tickets on the same airline when you travel because after 2 trips to Rio de Janeiro from the United States you will have accrured enough miles to achieve elite status on the airline and perhaps a free flight! Just be sure to sign up for the free, frequent flyer program that all the major airlines have and provide the number they give you whenever you fly. When you check in for the flight do make sure they have entered your number because at times the consolidators may forget to enter it.
Oh yeah, make sure you get a good seat on the plane by going to www.seatguru.com and seeing where your seat is located. If the seat is bad, call the airline and get another assigned, or go online to the airline website and change it yourself.