Most travelers in Peru will be looking to use the internet to stay in touch with fellow travelers and with friends and family back home. Your hostel or hotel will probably offer wither a communal desktop computer for guests to use in the common room, or wi-fi connection. If your hostel or hotel does not offer these services, don't worry. Chances are there will be a cyber café close by where you are staying. To use 15 minutes or half an hour of internet at a cyber is normally around S/.0.50 ($0.20).
If you want to use your regular phone to make international calls, check your plan and the company you use to see what international calling options they provide. As more and more people travel, some companies are offering better and better international plans. Some, for example, might allow you to receive text messages for free, or even for the sender to send them internationally to you for free. Skype, though, is the best option! If you can get wi-fi on your phone, use skype to call home for free.
If you are planning on staying for a longer visit in Peru, consider getting a local cell phone to stay in contact with your Peruvian friends or host family. Claro and Movistar are the two main phone companies in Peru, although Entel is also starting to expand and move up to join their ranks as a third major phone service provider. Claro has the reputation for offering a better phone service, while Movistar supposedly offers a better TV and internet option. Both, however, suffer from intermittent signal service throughout Cusco and before you make a decision you might want to ask friends with Claro and Movistar to see which one gets more bars where you live or work. Sometimes Claro has service in places where Movistar doesn't, and visa versa.
Once you've made your decision on which company, visit any Claro and Movistar store, they are literally everywhere, to see what your options are. You should be able to find a cheap phone for around S/.50 ($20), and can buy a chip for S/.10 ($3). The plan you will receive with this type of chip is called prepago, or 'prepaid.' Rather than pay a fee per month for a certain minutes plan, you buy recargas, or recharges or refills, whenever you need more phone minutes. So you make a recarga of any amount you like, S/.5 – S/.20 is the most common, and use those minutes until they run out and you need to make another recarga. It's very simple, and you don't need to visit a Claro or Movistar store to make a recarga. Most corner stores offer the service and they are easy to find, just look for a cardboard Claro or Movistar sign hanging up outside the doorway or window.