The Templo Mayor "Grand Temple or Major Temple" of the Aztecs was an incredible building, it was the central place of the city/island of Tenochtitlan. There are many accounts from the Spanish conquerors about it, and based on those descriptions—and a lot of archaeological research—it's possible today to have a vague idea of the splendor and magnificence of a place that was bigger and richer than the Emperor´s own palace. Just imagine that!
What you will find at this archaeological site is the mere remains of the basement of such a wonder or the ancient world, the reason is that the Spanish conquerors decided to destroy every trace of the temple to force the indigenous population to forget about their Gods in favor or Christianity. The stones used to build the Templo Mayor were used to construct the cathedral that you can see in front. All the incredibly detailed carved statues were sanded smooth and used as filling for the construction, and after many centuries chance made possible to find a lot of treasures hidden deep in the floor of the new city.
What you see in the museum is just a small, very small fraction of all the treasures of the Aztec Empire. Trying to imagine what is lost is mind-numbing.
Also you can find incredible pieces in the Anthropology Museum of Chapultepec. Those are not from the Templo Mayor, but of the general area of the old Downtown Tenochtitlan, which was full of temples and palaces.
Quick Tips:
If you are going to visit, reserve many hours of your time in the crazy paced city. There are so many things to see that you will have a hard time trying to be at 10 places at the same time.
Bring a wide rimmed hat and use sunscreen (less than 10 is useless, go for a 15 or 30) as even in winter you can get a nice sunburn for staying a couple hours watching the outdoor area of the site.
Some people recommend visiting the museum first so you have a better idea of what are the ruins you see, is up to you. Just be careful not to exit the site once you get off the museum and make it clear to the guards.
You will find a nice bookstore before the entrance/ticket booth. It is better to get back there after you finish your tour in the museum, but it will be tricky as you don´t use the same streets once you reach the exit.
All museums in Mexico are closed on Mondays so plan carefully, only the Pyramids of Teotihuacan are open that day. Take advantage.Best Way To Get Around:
The museum is located on a side to the Cathedral and just half a block from the main square of the city "El Zócalo," or "Plaza de la Constitución;" the second name is not very common, so stick to the first if you are arriving by taxi or are asking for directions.
There is a very convenient subway station (Zocalo, of course), just try not to use the subway during rush hours (inbound from 6 to 9:30am, and outbound after 5:30pm).
Lots of "Microbuses" arrive here, Zócalo would be in the windshield, but I don´t recommend them as their not the safest way of transportation, but if you are the adventure lover just don´t wear expensive jewelry and take good care of your wallet, don´t carry your passport with you, another kind of official ID is better (drivers license for example).
If you are lodged at the touristic zone, you have a great option, use the Turibus, a double-decker red bus that leaves from Auditorio Nacional every 30 minutes and for a flat daily fee you can board and unboard at any stop for the whole day. This will take you along Reforma Avenue, Avenida Juarez and Av. Madero rigth to the Zócalo.