The rule first: do not hail a taxi on the street. Use Uber, DiDi or Cabify, or a sitio rank. At the airport, buy an authorised taxi ticket at a booth inside the terminal. This is the most repeated advice about Mexico City and it is repeated because it is right.
Metro. Twelve lines, a flat fare of a few pesos to anywhere, and one of the cheapest systems in the world. Stations have pictograms as well as names, designed in 1969 so that everyone could navigate. The first carriages are reserved for women and children and this is enforced. Large luggage is not permitted.
Metrobús. Bus rapid transit in dedicated lanes. Line 1 along Insurgentes is the useful one for visitors; Line 4 serves both airport terminals and takes luggage.
Movilidad Integrada card, bought at station machines, covers Metro, Metrobús, Tren Ligero, Cablebús and RTP buses.
Cablebús. Two cable-car lines serving hillside districts, ordinary transport with extraordinary views.
Ecobici for bikes, and Paseo de la Reforma closes to cars on Sunday mornings for cycling and running.
Peseros — the green minibuses — are cheap, ubiquitous and hard to use without Spanish.
Driving is a poor idea: severe traffic, and Hoy No Circula restricts vehicles by number plate on given days, including hire cars.
For the detail, see Getting Around Mexico City.