Make sure that you get to the airport early enough for your flight. As experienced travelers, we were told to be there one hour before departure for a local flight (to Mexico City). Just in case we got there a little before this time, but were told that the flight had closed ... the rule is that you need to have checked in at the desk one hour before departure! All luggage was searched before checking in (which takes a queue and some time) and of course you need to queue to check in. Take these into account in arriving at the airport so that you will be at the front of the check in line one hour before departure. Instead of an hour before departure, I suggest you get there 90 minutes before departure.
People coming out of Mexico must use an airplane. We have an International Airport.
The other way is by bus, but only if the trip is inside Mexico
For a tourist the best way to get around Monterrey is by taxi, but you can also use the subway for getting closer the place you want to go.
I have a very easy time getting to and from because I live in San Antonio and there is a direct flight, reasonably priced on Aeroliteral. However, you need to be able to fly in a small plane, because they are.
Your best bet is to hire transportation, and not necessarily a taxi. It is relatively easy to hire someone to take you around and then you don't have to worry about traffic, parking, getting lost, etc.
Monterrey has got an airport for inner Mexican and US flights. From other Mexican cities you can get there by one of the excellent buses (from Mexico City it´s 12 hours for example).
Monterrey has got 2 subway lines that will get you around in the very center only. They have a great number of local bus lines, however there are no bus plans, so just ask the driver. Be sure to count your change! There are bus stops but usually you can also just stop a bus on the street. To get off you´ll have to pull the line at the window.
If you´re unsure and you´ve got money to spend better take a taxi (never alone at night as a girl though!).
I think the best way to get there is by airplane, both airlines, Mexicana and AeroMexcio are good choices to use.
This place is about 1:20 min flying from Mexico City.
To move around Monterrey i think the best way is by taxis cause to be honest as there are a bunch of different high ways or free ways you can get lost pretty easy if you dont know the place..