The buses are comfortable - much more comfortable than planes. Bathrooms, a/c and enough legroom not to get cramp. You can find out schedules and prices on www.ado.com.mx (remember that full schedules may not be available online until 30 days before departure).
You might want to ask in the Puebla forum, but the times I've gone, I've taken the bus to Puebla, Quatro Poniente station; from there, it's a relatively short cab ride (15-20 minutes in light traffic?) to the Centro.
I dont remember the terminals, but I recall arriving at one, and leaving from another (probably because I arrived from Tlaxcala and went back to Mexico City).
If by any chance you are leaving for Puebla straight from the airport, there are buses there (Estrella Rojo, I think)- you dont need to go into Mexico City to get to Puebla.
You already have some good responses. The buses are very good if you go first class and there are even higher class buses for more money but the first class ones are plenty good plus the more expensive ones don't go as often. One complaint from some people is that the A/C is sometimes too cool for some people so you might want a jacket or sweater with you. Others complain about the movies but if one is shown that you would like to see then that is OK.
Puebla (our favorite city in Mexico) is only about two hours away from Mexico City and, has already been mentioned, there is a bus that goes there at least every hour from the airport but it is a bit more expensive than the regular first class buses from DF.
Puebla has two bus stations and from each one you will want to take a city bus if you don't have too much luggage or a taxi to the centro historico (city center).
Oaxaca (lovely city) is farther away with a bus ride that must be, if I remember correctly, roughly seven hours or so from Mexico City and it goes through lots of rough looking topography with a sparse population. There is one main bus station that is north of the city center and about a mile away to Oaxaca's center.
A bit of a recommendation- go to Puebla first since it is on the way to Oaxaca and you can get a bus from Puebla to Oaxaca which makes that ride a bit shorter (or do it vice versa).
Thank you to all for your replies and Unlcelouie for a detailed response. Much appreciated.
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