Your best bet is to save the contact number as '+' followed by country code. In the dialer, you can also long-press '0' to generate a '+'. This will dial the destination numbers correctly regardless of where you're calling from.
Dialing within North America: +1
Dialing from North America to anywhere else: 011 (or +) then country code
Dialing from elsewhere to North America: 001 (then 10 digits) or +1 will work
Dialing from outside of North America to another country outside of North America: verify with local provider. Often it's 00 followed by country code. Again, + then country code will work on a cellphone.