The capital city of Lima has the Jorge Chávez International Airport with frequent flights all over the world. Main airlines are American Airlines, Delta, JetBlue, Lan, Lan Peru, United, Iberia, Copa, Taca and others. There are non-stop flights to Lima from Atlanta, Dallas, Houston, Los Angeles, Miami, Fort Lauderdale, Newark, New York City, and San Francisco in the United States. There is also a non-stop flight to Toronto, Canada with Air Canada. There are five different airlines that offer non-stop service to Europe. In the future there may be non-stop flights from Oceania or Asia but for now travellers usually connect through Los Angeles non-US citizens have to pass immigration even for transfer, consuming 1-2 hours - so ensure your stop-over is long enough! or through Santiago de Chile.
There is an internal flight tax, around USD6, same conditions as the international one.
When booking domestic flights, there are several Peruvian travel agencies that can get you your plane tickets for the "Peruvian price" for a fee of about USD20, you'll notice that the prices can vary by several hundred dollars for the SAME flights when looking at LAN's Peruvian site and the LAN.com site. You'll find that if you try to book the cheaper flights from the Peruvian site, they won't accept payment from American bank accounts this is why you do it through a Peruvian travel agency.
The city of Iquitos has flights to Leticia, Colombia with AviaSelva. They have a USD10 departure tax.