Benito Juarez airport (MEX) serving Mexico City is modern and efficient. There are two terminals linked by a monorail that can only be used by passengers who have a ticket, boarding pass or eticket ref number. Others need to take a bus or taxi (see below): it is too far to walk. 

The newer Terminal 2 is used by Aeromexico and (mostly) its partners in the SkyTeam alliance. Terminal 1 has sections for both international and domestic flights. International visitors will be given an arrivals card (FMT) and a customs form on board their flight. Once in the terminal, go to the correct immigration area. There are separate areas for North America, Europe, Middle East and Asia, and the Caribbean and Latin America. Present your FMT with your passport. Be sure to hang on to the portion of the FMT the officer returns to you as you will need to present this on departure and will be fined if you don't have it. Once you have collected your bags, hand over your customs form and then place your bags in the X-Ray machine and press the button indicated: a green light means you can go straight through to the arrivals hall, a red light will entail a visual inspection of your bags. In the arrivals hall, there are plenty of ATMs issuing pesos cash. In Terminal 1, baggage carts are free and cannot be taken past the Arrivals Hall, but there are plenty of porters available. In Terminal 2, there is a nominal fee for a baggage cart and it can be taken to the taxi rank or parking lot.

If you are continuing on to another destination in Mexico on the same carrier you generally do not need to recheck your luggage as you would in the US.  However, it would be well to double check with your airlineI

The airport has all the usual facilities, including left luggage lockers. If you are heading in to Mexico City itself, the recommended, and safest, way is to take an authorised taxi. You will see signs pointing to the desks where you pre-pay your fare by zone. Go here for information (in Spanish) about current prices. Most areas of interest to visitors will be in Zones 3 (Zócalo and Centro Histórico), 4 (Reforma, Zona Rosa), 5 or 6 (Condesa, Roma, Polanco). There are a number of companies, all costing the same; there are standard limousines for up to 3 passengers as well as larger vehicles. You will be directed to the departure area: the vehicles are all official airport taxis, with an aeroplane logo. Do NOT accept a ride from any of the touts who might be hanging around the terminal, or attempt to take a non official taxi. As a more expensive alternative to a taxi, your hotel can generally send a car to the airport to collect you.

There is a subway/metro station at Terminal 1. Turn left outside the terminal building and walk to the end near the main road and then down the steps. This is only advised if you are confident in Spanish and have minimal baggage. The flat fare is 2 pesos.

There are direct buses from the airport to Puebla, Querétaro, Toluca, Cuernavaca Tlaxcala, Pachuca and Cordoba. Go here for timetables and prices. They run every 30 to 40 minutes until mid/late evening. There is no need to pre-purchase tickets. Look for the signs saying Transporte Foréano/Terrestre. In T1, turn left in the arrivals hall and then go up the ramp to the next level near Gate 6. Walk straight in front of you until you see a footbridge. The ticket desks are across this bridge. There is a nice waiting room and the departure bays are down the escalator. Be sure to be at your bus about 15 minutes before departure to check in your bags and for the security check. In T2, turn right once upstairs in the departures area and you'll see the bus departure bays at the far end of the terminal by Gate 4. All the buses leave from here initially and continue to T1 before heading to their final destination. If in doubt about how to get from arrivals to the bus bays, hire a porter.