Question

What common religious practice was shared amongst the mesoamerican civilizations

Answer 1

Mythology and worldview
Further information: Mesoamerican religion, Mesoamerican creation myths, and Mesoamerican world tree
See also: Aztec religion, Olmec mythology, Maya religion, and Maya mythology

The shared traits in Mesoamerican mythology are characterized by their common basis as a religion that although in many Mesoamerican groups developed into complex polytheistic religious systems, retained some shamanistic elements.[25]

The great breadth of the Mesoamerican pantheon of deities is due to the incorporation of ideological and religious elements from the first primitive religion of Fire, Earth, Water and Nature. Astral divinities (the sun, stars, constellations, and Venus) were adopted, and represented in anthropomorphic, zoomorphic, and anthropozoomorphic sculptures, and in day-to-day objects[this quote needs a citation].

The qualities of these gods and their attributes changed with the passage of time and with cultural influences from other Mesoamerican groups. The gods are at once three: creator, preserver and destroyer, and at the same time just one. An important characteristic of Mesoamerican religion was the dualism among the divine entities. The gods represented the confrontation between opposite poles: the positive, exemplified by light, the masculine, force, war, the sun, etc.; and the negative, exemplified by darkness, the feminine, repose, peace, the moon, etc. (European ideology, Manichaeism)[this quote needs a citation]
The xoloitzcuintle is one of the naguales of the god Quetzalcoatl. In this form, it helps the dead cross the Chicnahuapan, a river that separates the world of the living from the dead.
Aztec Jaguar warrior, by George S. Stuart

The typical Mesoamerican cosmology sees the world as separated into a day world watched by the sun and a night world wached by the moon. More importantly, the three superposed levels of the world are united by a Ceiba tree (Yaxche' in Mayan). The geographic vision is also tied to the cardinal points.

Certain geographical features are linked to different parts of this cosmovision. Thus Mountains and tall trees connect the middle and upper worlds; caves connect the middle and the nether worlds.
Sacrifice
Ritual human sacrifice portrayed in Codex Laud

Generally, sacrifice can be divided into two types: autosacrifice and human sacrifice. The different forms of sacrifice are reflected in the imagery used to evoke ideological structure and sociocultural organization in Mesoamerica. In the Maya area, for example, stele depict bloodletting rituals performed by ruling elites, eagles and jaguars devouring human hearts, jade circles or necklaces that represented hearts, and plants and flowers that symbolized both nature and the blood that provided life.[this quote needs a citation] Imagery also showed pleas for rain or pleas for blood, with the same intention – to replenish the divine energy.
http://en.wikipedia.org/wiki/Mesoamerica#Mythology_and_worldview

Answer 2

Divine beings and Gods controlled the universe and interacted with men. A shaman or priest class acted as intermediaries between the common people and their Gods and spirits.There were three tiers of existence : the physical realm they inhabited, an underworld, and a sky realm. They considered certain man- made and natural places sacred.