Take the Blue Line (#2) of the Mexico City metro to Tasquena (the last station). Transfer to the light rail (Tren Ligero) and take it to the Estadio Azteca station. Get off on the stadium side and hop on a pesero (green minibuses) with "Ajusco" written on it (Ruta 39 if I remember correctly). After a winding road through Mexico City's southern suburbs, you'll arrive at the end of the line, a village called Santo Tomas Ajusco (if you're confused about which bus to take, you can ask the driver for the village by name). Next to the bus stop is a taxi sitio. Get a ride up to the trailhead, passing some nice views of the surrounding volcanoes from the eastern side of the loop road. Eventually, you'll come to a large grassy field (families will be here on the weekends) with an isolated restaurant and a police station (they're "monitoring the area"). Ask the driver to come back in a particular amount of time (2 hours is usually good, but you can modify it per your strength and level of acclimatization). This is important, since there's no telephone near the trailhead, the cell phone reception is touch-and-go, and the relative middle of nowhere in Mexico is not the best place in the world to hitch a ride.
Signs will guide you through a high-desert-type alpine forest to a fork. Here you can choose the normal route, which lazily winds its way up the mountain, or the "alpinismo" route, which goes straight up. The former is a straightforward hike, the latter involves a little scrambling (though it's not terribly difficult; I climbed it in tennis shoes) over "crushed graham cracker" type rock similar to that of the Cascade Range.
After a series of climbs and traverses, you reach the Northeast Ridge, which gives you your first good view of the crater. From here, a discernable trail follows the ridge, avoiding sheer dropoffs. You might find the occasional grazing livestock populating the hillside. After a while, the giant white cross that marks the summit comes into view. After about twenty minutes or so more of hiking, you reach it.
Waterproof jacket for afternoon rains, sunglasses, sturdy shoes, plenty of water, sunscreen. No technical climbing gear needed - it's a straightforward hike. If you're a map junkie and have $15 burning a hole in your pocket, you can buy the Guia Roji, a Thomas Bros.-like book that covers all of greater Mexico City and includes Ajusco and the surrounding areas in case you get lost or want to explore.
Late afternoon storms are very common in the Valley of Mexico (whose southern extent Ajusco marks), so I wouldn't start out later than 1:00. Lightning is very common, and the ridge (and the entire mountain, for that matter) is completely exposed.
If you're wanting to climb Ajusco for the views, you will more often than not be disappointed. Smog frequently blankets the valley, and ever-present clouds usually take care of the rest. If you want to see the city, I'd recommend going to the top of the Torre Latinoamerica (the big building in the historic center). For Ixta and Popo, Amecameca or Puebla to the east are probably better bets.
Right now (August 2004), the exchange rate is about 11.4 pesos/dollar. Here are the one-way costs:
Metro: 2 pesos
Light rail: 2 pesos
Pesero: 4.5 pesos
Taxi: 40 pesos (plus a nominal fee if the driver has to wait)
Ajusco is probably the cheapest to climb of Mexico's 13,000+ mountains.