How to Arrive:
From the airport in Mexico City, the most economical way to get to Tepoztlan is the following:
From the airport, take a taxi to the Taxqueña (taskenya) bus station. After you pass through baggage claim in the airport, there will be stands selling rides for "safe taxis" or "taxis seguros", which basically means that they are registered taxis and they will charge you a flat rate to get to the bus station (I believe now it's around 200 pesos, which is 15 dollars or so). They will give you a ticket to give to an attendant just outside the airport, and the attendant will help you get the next available taxi and tell them your destination. You won't have to pay the taxi driver anything, tipping taxi drivers isn't common in Mexico. The ride to the bus station in taxi is about 30 minutes. Once you get to the bus station, find the ticket booth for the company Pullman de Morelos. There you can buy a ticket for the next bus to Tepoztlan. The busses go by every half hour, starting at 6 am and ending at 9:30 pm. Bus tickets cost around 100 pesos (7 dollars). The bus ride is about an hour long and the bus will leave you at the gas station in Tepoztlan. From there, there are lots of taxis that can take you to your final destination in Tepoztlan.
As a side tip, it's recommended that you sit towards the front of the busses if possible.
There are also taxis that go from the airport to Tepoztlan, but they will probably be pretty expensive.