Getting around Mexico city offers several possibilities, Buses are the cheapest way of getting from place to place, and are comparatively cheap, and correspondingly crowded, dirty and uncomfortable. Most convenient are the VW beetle taxis that scream from place to place with scant regard for speed limits or lane discipline. Despite the fact that Mexican taxi drivers have a reputation for being notoriously relaxed in their driving, as a rule passengers will arrive at their destinations safe, but shaky.
If you plan to hire a car and tour the city yourself, don't.