How to call and use Cell Phones In Mexico. Long-Distance phones in Mexico
Phone Service In General
Mexican cell phone and land line phone service is quite good, these days. VOIP telephone service is everywhere in Mexico. Cell phone service in Mexico is good and reasonably-priced. Long distance calling to Mexico or from Mexico is cheaper, calling cards (Telmex calling cards or CogniCall) to or from Mexico is reasonably-priced. Long distance through broadband phone services or VOIP like Vonage have made calling to and from Mexico actually free. Yes, you can use any VOIP phone in your home in Mexico if you have a broadband connection. No, they will not ship a VOIP adapter to you in Mexico. You have to bring your adaptor down. If you sign up for Vonage on their refer a friend program and give them my number - 512-351-4058 I get a free month and you get a good deal. Sign up for Vonage.
Cell Phones In Mexico
Many US cell phone companies now offer a Mexico calling plan. For about five bucks a month, you can call back to the States for a dime a minute. I do not know about Canadian cell phone companies.
If you want to get a US phone service with good service to Mexico, ATT has the best coverage (with TelCel). They have different names for their plans but there is a Mexico plan that is quite reasonable.
To call a Mexican cell phone from the USA
To call a Mexican cell phone number, add an extra "1" to the number when calling from the States.
To call a Mexican cell phone within Mexico
From a landline, add 044 to the city code + the number. If it is long distance, dial 045 - the city code - the number.
To call a landline within Mexico
Simply dial a 1 then the city code and the phone number.
If you have a Mexican cell phone in Mexico
To call from a Mexican cell phone from Mexico, if the call is local, just dial the phone number. If that does not work, try 045 + city code + phone number.
To call the USA or Canada
Piece of cake! Dial 00 then 1 (country code) then area code and number.
If you sign up for Vonage on their refer a friend program and give them my number - 512-351-4058 I get a free month and you get a good deal. Sign up for Vonage.
USA or International Phone Options
You can probably call home with your US carrier (ATT, Sprint, Verizon etc.). Just check for a plan that has good rates calling FROM Mexico. Lots have good rates TO Mexico, but put you on roaming while in-country. Believe me, that can be an expensive surprise.
If you have an unlocked phone or a GSM or if you want to buy or rent an international phone, you can get a phone or a SIM card from these people. 
Their rates for Mexico are not that great, but for Central America, they cannot be beat. And if you don't want to give your US passport number to some pimply-faced clerk at an Oxxo store, maybe they are worth it.
Get a Mexican Cell Phone - Maybe
Alas, in the summer of 2010, the Mexican government added a new wrinkle to getting a Mexican cell phone. There still are throwaway cell phones in Mexico that you can buy at many convenience stores, even from those associated with Pemex stations. They are about $20 or so.
But, now, you have to present your passport to the clerk who enters the passport number into a database (supposedly to cut down on drug dealers from buying them - hah!). In the first few months this was done (Mexicans show their identify card), the lists of identify cards and information were sold. Hmm.
This same scheme is being implemeted in the USA - you must present ID to get a disposable cell phone.
If you decide to get a Mexican cell phone, do so at a phone company store, not a convenience store. Activating them requires a little work and the phone clerk can do it for you.
Calling Mexico Without A Plan
I have never been a fan of plans. Wing it, I say. If you only occasionally need to call Mexico from the USA or Canada, try a calling card from the link below. The way it works is you buy a virtual "card," get a pin via email and dial an access number (usually an 800 number, but sometimes a local number where you live). Then you dial 01152 to get to Mexico then the phone number. Instructions are on the site. Caveat - all these cards and the ones sold in convenience stores, claim rates of 1.2 cents or 0.9 cents or 2.1 cents per minute. That ain' t true. They are cheap and the actual call does costs the stated cents per minute, but there are other fees.
Many of you come to this page directly. If you are all interested in Mexico, you will find much of interest on this site: spas, hot springs, driving, maps of Mexico and eclectic items you won't find elsewhere. Please peruse. If you are moving to Mexico, or driving to Mexico, remember, I am available for consultations.
Your best deal for residential long-distance phones in Mexico or in the U.S. is a VOIP phone. One advantage is that even if you live in Mexico, you can have as many US phone numbers as you want so family and friends can call you with no international charges.
Phone Service IN Mexico
Thanks to competition, you can now get a new phone line from Telmex in a matter of a few days -- in some cases -- and more often within a week or two-- if there is not already a phone line installed in your new home. If there is, the info below still applies. While you are still in the States, you have two main choices to get inexpensive long distance to Mexico and the world, as well as U.S. long distance.
When you rent or buy a habitat, if there is an existing phone line, the phone line comes when you buy or rent an abode. Seriously. I don't mean the physical instrument. The actual line and connection to the phone company.
Casetas de larga distancia (long distance offices) are almost gone now.
Today, to make a call in public you need a phone card to use the new phones. But since everyone except me has a cell phone, it is getting harder and harder to find a pay phone.
Calling Cards -- From Mexico to the world
To make calls from Mexico to the rest of the world via a pay phone you can use either a Telmex card (expensive but available everywhere in Mexico) or plan ahead and get one of the several calling cards from the company above. There are several different calling cards and pans.
Telmex only bills in full-minute increments and is more expensive than any other option (except for hotel phones).