In Europe the prefix for international calls is 00. So yes, you would dial 00 (for initiating an international call) 1 (for North America) 212 (e.g. NYC area code) 1234567 (phone number).
In contrast, in North America the international prefix is 011, while Japan uses 010 and there are several other international prefixes around the world:
List of international call prefixes - Wikipedia, the free encyclopedia
To overcome the inconvenience of those changing international prefixes, a universal prefix was introduced, the +. So when you dial an international number beginning with + instead of the local international prefix, it will work worldwide.
If you dial +1 212 1234567 it will work everywhere, no matter which international prefix is locally used. Therefore it's wise to save all numbers in international format with + as international prefix in your phonebook and so you will never need to care about the local international prefix anymore.