The Aztec Calendar
It should be noted that this section is almost entirely speculative. In Mesoamerica, every moment is defined by forces, natural and otherwise, that are defined by the gods. We do know, definitively, that the Tonalpohualli was used in divination, we just don't know exactly how.
But it seems to me that the Mesoamericans believed that knowing when a thing will happen determines in many ways what will happen. This really is not all that different, for the most part, from the astrology most everyone is at least somewhat familiar with, it just operates in a different way.
The chart showing the day-signs also shows that each day is ruled by one of the Teteo (the gods). In the same way, each of the weeks is ruled by one of the Teteo (An Aztec "week" is a series of 13 days beginning with a "1"), and so is each "hour" of the day and night (Mesoamerican days consist of 22 "hours," 13 of which are considered to be "day" hours and 9 of which are "night" hours, and the day begins at sunrise). All those are ruled by one of the Teteo as well, as are each of the "months" (20-day periods). The rulers of the months are given in the chart defining those months (see The Months of the Year and the Rites; the rulers of the weeks and hours are as follows:

 
Week of Ruled by
1 CipactliTonacatecuhtli
1 OcelotlQuetzalcoatl
1 MazatlTepeyollotl
1 XochitlHuehuecoyotl
1 AcatlChalchihuitlicue
1 MiquiztliTecciztecatl
1 QuiahuitlTlaloc
1 MalinalliMayahuel
1 CoatlXiuhtecuhtli
1 TecpatlMictlantecuhtli
1 OzomatliPatecatl
1 QuetzpalinItzcoliuhqui
1 OllinTlazolteotl
1 ItzcuintliXipe Totec
1 CalliItzpapalotl
1 CozcaquauhtliXolotl
1 AtlChalchiuhtotolin
1 EhecatlChantico
1 CuauhtliXochiquetzal
1 TochtliXiuhtecuhtli and Itzli
Hour Ruled by
1 DayXiuhtecuhtli
2 DayTlaltecuhtli
3 DayChalchihuitlicue
4 DayTonatiuh
5 DayTlazolteotl
6 DayTeoyaomiqui
7 DayXochipilli
8 DayTlaloc
9 DayQuetzalcoatl
10 DayTezcatlipoca
11 DayMictlantecuhtli
12 DayTlahuizcalpantecuhtli
13 DayIlamatecuhtli
1 NightXiuhtecuhtli
2 NightItzli
3 NightPiltzintecuhtli
4 NightCenteotl
5 NightMictlantecuhtli
6 NightChalchihuitlicue
7 NightTlazolteotl
8 NightTepeyollotl
9 NightTlaloc
Thus, at any given hour of any day of any week of any month, there are four sacred rulers - four sets of possibly conflicting, possibly conspiring, forces at work. At the seventh hour of the night on a day Nahui Coatl in the month of Toxcatl, the "month" force is Tezcatlipoca, the "week" force is Chantico, the "day" force is Chalchihuitlicue, and the "Hour" force is Tlazolteotl. There is an element of fate, of feminine fire, of flowing water, and of passion. And it represent a confluence of forces that will occur only once in any fifty-two year period. In the following year there wouldn't even be a day Nahui Coatl during Toxcatl.
It was also believed that the events of the world move in regular cycles. In the view of the Mesoamericans, then, understanding the flow of those cycles was seen as the key to understanding and even predicting events.
Clicking below will let you download a ZIP file containing a program to translate modern calendars and clocks into those used by the Aztecs. It's based essentially on Sahagun's "New Year" as Feb. 2 and the year 1519 as a year Ce Acatl; leap years are "tagged in" at year-end (Feb 1) and the movement of the numbers and signs suspended for a day at that time. Calculating the day or night hours will require looking up times for sunrise/sunset on a given day. The program is written in DOS, but runs fine under WinXP.

Download the calendar program (49K)

There's a readme included to explain how to use it. Guaranteed virus-free...