Visas
Tourists from North America, Australia, Japan, and the European Union (and many others, check with the nearest Peruvian Embassy or the Ministry of Foreign Affairs for most updated information, although in Spanish) receive a visa upon arrival for up to 90 days.

When entering the country, you need to pass the immigration office (imigracion). There you get a stamp in your passport that states the number of days you are allowed to stay (usually 90 days). You can no longer get an extension, so make sure that you ask for the amount of time you think you'll need. When those 180 days are up and you would like to stay for longer, you can either cross the border to a neighbouring country (Ecuador, Colombia, Brazil, Bolivia or Chile) and return the next day and obtain another 180 days or simply overstay and pay the fine when you exit. The overstay fine is only $1 USD per day overage, so if you stay 30 days longer it's $30. Many people do this, since it's much cheaper than leaving the country and returning.

You will receive an extra official paper to be kept in the passport (make sure you don't lose it!). When leaving, you need to visit the emigration office (migracion), where you get the exit stamp. Imigracion and migracion are found on all border crossing-points. Traveling to and from neighboring countries by land is no problem.

By plane
The capital city of Lima has the Jorge Chávez International Airport with frequent flights all over the world. Main airlines are American Airlines, Delta, Lan, Lan Peru, Continental, Iberia, Copa, Taca and others. There are non-stop flights to Lima from Atlanta, Dallas, Houston, Los Angeles, Miami, Newark, and New York City 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 travelers usually connect through Los Angeles (non-US-citizen have to pass immigration even for transfer, consuming 1-2 hours - so ensure your stop-over is long enough!).

For example, Iberia flies directly from Madrid to Lima, the trip lasting around 13 hours but it is not recommended. LAN and KLM flights are much better in quality. LAN and Iberia often fly in code share mode (1 plane, 2 flight codes) and check-in is in MAD and LIM chaotic - if you've a LAN flight, you may have to check in at Iberia service desk or the opposite way, sometimes they send you from one to the next and back, so just queue at the shorter service desk...

When leaving the country on an international flight you have to pay a departure tax. The amount changes, but expect it to be US $25-$30 or the equivalent in soles. This has to be paid in cash before entering the departure area.

There is also an internal flight tax, around 6 USD, 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 $20, you'll notice that the prices can vary by several hundred dollars for the SAME flights when looking at LANs Peruvian site (http://www.lan.com/index-es-pe.html). 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 $10 departure tax.

From Ecuador
Although Ecuador neighbors Peru, it is hard to find cheap flights connecting anything but the capitals. In particular, flying from Ecuador to Iquitos is not possible directly, nor can you travel directly from other large towns across the border.

By boat
The city of Iquitos in the Amazonas region has connections by boat to Leticia in Colombia and Tabatinga in Brazil (about 10 hours).