When I was in Tapachula I realized it was a mistake to travel there as touristic destination, however I took a taxi to go to Union Juarez and my trip changed, I met Lorenzo Robles a nice taxi driver (cell phone +9621364079) who showed me the archeological zone of Izapa and because of him I could visit the famous stone of the "tree of life". The day before several taxi drivers were so abusive charging me over $100 mexican pesos/hour because "if you are out of town this fare does not apply", why not? if I was always going to come back¡ but Lorenzo drove to Union Juarez (50kms away in te mountain)and did not charge me any extra, besides that he was explaing everything about the area , having a tour guide for the price of a taxi driver..if you ever go there dont hesiate on reaching this decent and well-educated man.
If you arrive by plane, you'll need to move from the airport to downtown. They have taxi cabs you can ride, they're safe and fast but they're expensive (around the equivalent of 12 US dollars for a single ride, usually no more than 15 mins. long); but there's the option to walk a few meters to the road that connects Tapachula with Puerto Madero (the nearest beach), and you'll be able to find "collective taxis" (which hold 5 people) and buses that will take you to downtown for $10 Mexican pesos (less than 1 US dollar).
Moving around Tapachula is easy, distances are rather short and you can walk. But sometimes the weather is way too hot, so you may want to take a bus... they charge you a small fee per trip (around 4 Mex. pesos, 40 cents of a US dollar), no matter where you're going as long as it is within their route. Taxis within the city aren't too expensive (they usually don't have a meter but charge a fixed fee depending on where you're going -- it's a good idea to set it with the driver in advance) so they're a good option too.
Since Tapachula isn't the capital of the state of Chiapas and it is a very small town indeed, I honestly thought they had no airport.... but they do!! And it's an International Airport... You can fly to the main cities in Mexico from there. It's a very small airport but some important airlines have several flights a day to and from there.
If you're travelling from Mexico City (most of the connection flights stop by here), you can buy a plane ticket with Aeromexico or Aviacsa airlines... both are very good and the price of their tickets is the same (around 300 USD round trip to and from Mexico City.... if you're going farther the prices can be up to 600 USD or more).
The bus service all around Mexico is pretty reliable and comfortable, so if you want to pay less to get to Tapachula and you're not in a rush, you can ride a bus instead of flying. They have normal and deluxe services (the latter costing around 70 USD, one-way trip, so the former must be even cheaper), and the average time of the journey between Mexico City and Tapachula is 17 hours (with several stopovers).
OCC (Cristobal Colon) and its "Plus" service are the bus lines that can take you to Tapachula from Mexico City and viceversa.