Within cities, there are various options, and they are all cheap. In Mexico City, Guadalajara, and Monterrey, the cheapest and fastest option is probably the metro. A second option is to take a city bus. Different types exist in different cities. In Mexico City, for example, you can take a Metrobus, which follows a dedicated lane and you thus avoid being stuck in traffic. Another type of transportation is the microbus (also called colectivo, combi, or pesero), which stop almost at any street corner. Route information is usually displayed on the window.
Be aware that public transportation in cities can get crowded, especially during rush hour in the bigger cities.
To travel between cities, Mexico has an excellent bus network with comfortable, frequent, and reasonably priced bus services. There is only one passenger train in Mexico, "El Chepe," which travels from Chihuahua to Los Mochis, passing through the Copper Canyon.