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 : it is too far to walk.  There are special red buses that takes you from T1 to T2 for just 5 pesos (50 cents usd) each way

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 two separate areas: one for arrivals from North America, Europe, Middle East and Asia, and the other for arrivals from 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 to destination outside of Mexico, Area K has gates for international flights. 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 U.S.  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. At both terminals, you will see signs pointing to the desks where you pre-pay your fare by zone.  They all cost the same, but be sure to specify a sedan, unless there are more than three of you. Most have a website which enables you to enter your destination to find out the cost. Once you have paid and received your coupon you will be directed to the departure area. 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.

Authorized Airport Taxis companies: Yellow Cab AeropuertoTransfers-USA, Nueva Imagen, Porto Taxi, Sitio 300, Comfort, Excelencia. HOWEVER, the people at the booth will often try to sell you a more expensive ticket (normally, for a large van). DO NOT FALL FOR THIS. Say you want a sedán (SAY-DAN) and anything headed to downtown will be UNDER 200 pesos.  Getting a taxi from Mexico Airport can be a harrowing experience.  If you have the time before you leave it is worth searching online and prebooking your taxi prior to arriving, some companies, such as  Mexico Airport Transfers, have an option to book and pay from the comfort of your armchair.  Often the cost is not a lot more than getting a taxi once you're at the airport, and the safety and peace of mind makes it worthwhile to some. There is no difference in price among the companies, but in the number of cars they operate. So what company you chose determines how long you have to wait. From subjective impression, Sitio 300 appears to be the best.  

There is a subway/metro station at Terminal 1. From Terminal 2's international arrival to Terminal 1, go one floor up and take the free airport train (need to have the boarding pass to take the train). At Terminal 1, go outside the terminal building from Gate 1 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 5 pesos. A more comfortable and still inexpensive route into the centro histórico is on the metrobus, line 4. This runs from both terminals. The fare is 30 pesos, but you have to pay an additional 10 pesos for the pre-paid smart card. This card can be used on all the metrobus lines and on the metro as well. The buses have luggage space and a cop on board and video surveillance.

There are direct buses from the airport to Puebla, Querétaro, Toluca, Cuernavaca Tlaxcala, Pachuca and Cordoba. 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.