00 ( zero zero ) is the International Access (Dial) Code used to call overseas from 'within' Peru. 

51 ( five one ) is the International Country (Calling) Code for Peru.

Then you will need to add the city code, being the most important :

To make national phone call within Peru you need to dial : 0 and then the city code

To Make an International phone call you need to dial : 00 and then the country code

To obtain phone number information  dial : 103

Emergency phone number is :  105  (not 911)

In April 2008, the dialing pattern changed for cellular phones in Peru.  All cell phone numbers are now 9 digits, and always start with a 9 as the first digit.  Previously, cell phone numbers were either 7 or 8 digits.  For cell phone numbers in Lima, the only change is to put an additional 9 in front of the old 8-digit cell phone number.  The dialing patterns for cities outside of the Lima area vary, and you may need to ask locally if you need to get an updated number.

If you have an unlocked GSM cell phone that includes the 850mhz and/or 1900mhz bands, you can purchase a prepaid SIM card upon arrival to use in your phone.  You will get a local 9-digit cell phone number and can immediately make and receive calls while in Peru.  Movistar has superior service and is in the 850mhz band. Claro has acceptable service, and is in the 1900mhz band. As of March 2009, you can purchase a SIM card for 15 Soles at many vendors, including the big department stores Ripley and Saga Falabella.  All incoming calls and text messages to cell phones in Peru are free. Cell phone rates have come down a lot in the last year, and now both Claro and Movistar now charge 50 centimos per minute for outgoing local calls for newly purchased phones and/or SIM cards.