By bus
TuriStar and Estrella Blanca from Mexico City are the most comfortable and most expensive way to get here $500-900, 12 hr, traveling via Acapulco. These buses only leave from the South Taxqueña bus terminal. Other first class buses leave from both the North and South terminals, traveling via Puebla and/or Oaxaca City, and taking several hours longer than the buses via Acapulco. The quickest 5-6 hr service, but least comfortable transport from Oaxaca is by van called suburban in Spanish. There are several companies $140. More comfortable but longer are the buses leaving from the 2nd class bus station. Do not take a 1st class bus because the trip is over 15 hr - it takes the longest route. 2nd class buses take around 7-8 hr. There are also many buses from Acapulco.
By car
Driving to Puerto Escondido is only advisable if you have experience with windy, poorly-maintained mountain roads. That said, it is an exhilarating, scenic drive from any direction. The roads that connect Puerto Escondido to Acapulco and Oaxaca are both narrow, twisty 2-lane roads in poor condition, that traverse the sparsely populated Western Sierra Madre. Driving your own car will not save you much time over taking the bus.