The best time to visit Mexico City is between March and May, even though the streets are pretty crowded this time of year. Your trade-off is beautiful weather, especially considering the city's winters can be really chilly and the summers can be really rainy.
Advance booking is the best way to get cheap flight to Mexico City. Book 4 to 6 week in advance to grab cheap flights. Airlines such as Aeromexico, US Airways, American Airline, Delta Airlines and United Airlines offers great discounts on airline tickets. From the airport to city take taxi or Bus.