The vast majority of Peruvians and budget conscious travelers use various forms of ground transportation. Keep in mind that air travel can be much cheaper when purchased in Peru or through knowledgeable agents than when purchased online or through U.S. sources.
Virtually all flights within Peru originate in Lima (although you can sometimes fly directly from one city in the South – Arequipa, Cusco, Puno – to another) and there is little choice in air carrier. For most places its pretty much Lan or Lan at this point (Peruvian air carriers have changed a lot during the past couple of decades!). Service is quite variable, and there isn’t much you can do about it.
Aerocondor serves the Nasca region from Lima, and they’ve been trying to expand to other areas as well (you can book online, but only in Spanish at www.aerocondor.com.pe
Note that tickets for flights within Peru are sometimes significantly more expensive on internet travel services and from travel agents in the U.S. who do not work regularly with the Peruvian carriers than they are when purchased in Peru. If you are concerned about prices, I recommend that you go through a travel agent with ties to an agent in Peru, or take your chances when you get there. A word of warning about buying airline tickets in Peru, however: make sure you get them from a reputable travel agent (the less serious ones sometimes fail to get a confirmation from the airline), or from the airline itself. If you are on a budget but you have plenty of time it can be worth your while to wait to decide on travel modes until you get to Peru and then seek advice from fellow travelers, and perhaps stop in at the South American Explorers Lima clubhouse. Buses are an option too (see below, but I don’t recommend them for travel from Lima to Cusco).
Although it can seem silly, I still recommend that you reconfirm each flight with around 24 hours to flight time, and don't be surprised if the schedule has been changed. If your Spanish isn't up to the phone call either go to the airline office or get help from someone at your hotel. Flights can be overbooked, and although tourists are less likely to be bumped than others, it still happens.
When you fly in Peru, keep in mind that flights can often delayed, sometimes for hours. Peruvian carriers have a small number of planes and they are scheduled very tightly each day from dawn to late night. If there is bad weather in Cusco, for example (where most of the early morning flights go) it destroys the airline schedule for the rest of the day. When I go to airport in Peru, I try to take a very relaxed attitude, food and water to last me most of the day, and plenty to do while I wait.
The Peruvian airlines almost never tell you what is going on when planes are delayed, so keep asking. They occasionally take care of their delayed passengers by providing refreshments at the gate, but there is rarely enough to go around, so those sitting closest to the gate agents usually have first crack at the Inka Cola. If something really bad happens to your schedule, your luggage, etc., particularly if it seems to be at least partly the airline's fault, don't be afraid to complain. Try to do your complaining in a really nice way though, explaining that you are a tourist, outlining the problem, and asking if there isn't anything they can do to help you. If you are not satisfied, call the toll free number that you are given as you enter Peru and make a complaint. I don't know if it really helps, but the government agency that takes the complaints says that they impose sanctions and fines on airlines and others with too many complaints, and the agents they send to take the complaints seem to be very nice and quite professional.
There is also a lot of ground transportation available in Peru, and this is what is used by the vast majority of Peruvians, as well as the most budget conscious tourists, to get around. See the various guidebooks for more information. Colectivos, buses, and trucks make for colorful and cheap travel, but they're not for everyone. Express buses (Royal Class, Imperial Class, etc.) are considerably quicker and more spacious than other buses, although they are more expensive.