On August 3rd, 2019 the dialing rules in Mexico changed in order to simplify the complicated system that was in place. The protocol is now similar to the ones in the US and Canada.
The most important change that was made is that service prefixes are no longer needed. Before, it was necessary to dial (01) for domestic long distance numbers, and (045) or (044) in order to call cell phones from landlines. The (1) that was used to call a Mexican number from abroad is no longer needed. The only thing that is needed now is the country code (+52). Here are the formats to call from abroad:
So, for example, if you were to call Mexico City whose city code is (55) you would have to dial 52 + 55 + local 8 digit number.
If you’re calling from national territory you just have to dial the area code + the local number. For example, if you’re calling Monterrey whose city code is (81), you would dial 81 + the local number.
For a full list of area codes, visit this website.