Getting to Cuernavaca is uncomplicated, but beware with the traffic in the Mexico-Cuernavaca-Acapulco toll way on Friday and Sunday afternoons. Several tourists tend to travel in those days, if you do not want to spend more than 2 hours try to choose other days for your traveling.
Viva Aerobus is a Mexican airline that offers not expensive tickets, around $45USD, when flying from Tijuana or Monterrey, though the airport is not that close to Cuernavaca, expect to pay some extra money for the taxi to Cuernavaca's central square.
There are various bus companies operating routes to Cuernavaca. Busses run from Mexico City's main bus stations in the North, South of the city and Airport. Busses run on every 20 minutes approximately and tickets charge around $68 pesos (USD$ 6.09). Pullman de Morelos runs the most regular routes. Busses are modern and secure and come equipped with air conditioning, toilets, and a movie during the trip. When there is no traffic the trip takes around 1 hour.
Take the Mexico-Acapulco expressway south from Mexico City for an hour and a half from the international airport. The toll road costs $85 pesos (USD$ 7.62) or there is a free road which is less well maintained.
Busses cover almost entire city and surroundings, it cost about $4 pesos (USD$ 0.36) per trip. These are not predominantly cozy, but are reasonably secure and frequently used by the many foreign language students in the city. On the other hand, there are several taxis which are available on the street or you can order one by phone. The biggest radio taxi firm in Cuernavaca is Citlali, and every one of radio taxis are safe, independent taxis are a little more dangerous. Taxis in Cuernavaca do not have meters and prices need to be arranged before getting in the taxi. During the day most destinations will not cost you more than $45 pesos (USD$ 4.03). At night prices sky-rocket and trying to get a taxi in the early hours of the morning will frequently charge considerably more.