I am not up to speed on the specifics of chronology in Old World civilizations, but for the sake of simplicity lets assume we're talking about the period from 3,000 BC to 1,000 BC. This covers most of the origins of complex societies in the Indus and Yellow river valleys (I think), with the latter portion of this period being considered the "height" of those civilizations.
In Mesoamerica and the Andes this corresponds to the Late Archaic to Initial/Early Formative Periods, when the very first complex societies were beginning. In the Andes, this was the period of the Norte Chico Civilization, while in Mesoamerica the latter portion of this period would be contemporary with the Mokaya culture.
The Norte Chico civilization is the oldest known civilization in the Americas. At the time, agriculture was not widespread. The people of the early Norte Chico region did have domesticated cotton and some supplemental agriculture, but it was not their main means of subsistence. They also did not have ceramics, and instead used baskets for storage and transportation. This makes them somewhat of an oddball among early civilizations, as most early civilizations arose after the invention of ceramics and the widespread adoption of agriculture (which is further proof that there are exceptions to every rule).
Instead, the people of the Late Archaic/Initial Period Norte Chico region relied on fishing for the bulk of their subsistence. Despite this, they built large monumental architecture (including earthen pyramids) and large public plazas. Research on them is still in its infancy compared to other early civilizations, but Haas and Creamer (2006 - JSTOR link) argue that the pyramids and plazas acted as the center of a religious/ceremonial tradition for the many fishing communities up and down the coast of Peru. Fish was/is an abundant resource in the region thanks to the Humboldt current, and fishers provided food for the people living in the cities/ceremonial centers located along the river valleys. People in the rivers in turn farmed cotton for the making of cloth and baskets that were exchanged with the fishermen. All partook in public ceremonies in the plazas.
The Mokaya, like their Andean counterparts in Norte Chico, also took advantage of maritime resources along the Pacific Coast, in this case from the rich estuaries found in the Socanusco region of souteastern Mexico. The largest and best studied Mokaya site is Paso de la Amada (Blake 1991 - Google Books Link.) Unlike the slightly earlier Norte Chico civilization in Peru, the Mokaya had both ceramics and subsistence agriculture, although neither were as widespread as they were for later Mesoamerican civilizations. There's been a lot of scholarly debate about whether or not there was a clearly defined social elite among the Mokaya. Blake (in the book chapter I linked) seems to take the stance that there was a hereditary noble (or "chiefly" even though I hate that word) class. Others disagree, and suggest status differences were more fluid at this point in time.
Regardless, Mokaya society could perhaps be described as theocratic; there were some civic buildings but most of the public and monumental architecture is religious in nature. Alcohol consumption appears to have been a part of religious activities, and it is among the Mokaya that we get the first ballcourts in Mesoamerica. The Mesoamerican ball game would become a standard feature of later Mesoamerican civilizations including the Maya and Aztecs where it had both political, entertainment, and religious characteristics. Mokaya pottery is also relatively rare and extremely elaborate in comparison to later Mesoamerican pottery, which suggests that it may have played more of a role in feasting than regular everyday use.
The Olmec civilization in Mesoamerica and the other early Mesoamerican civilizations (like the Preclassic Maya, Formative Period Zapotecs, and early Central Mexican cities like Cuicuilco) came to prominence as the Indus Valley civilization was declining (specifically ~1200 BC). It was during this period (the Middle and Late Formative) that you saw the growth of the first true cities in Mesoamerica as well as the development of long distance trade networks and shared art styles. The next major Andean civilization, Chavin, came to prominence some what later after the Indus Valley civilizations had declined (around 500-400 BC).
In the northwest, the 3000-1000BC period (to use the chronological slot that /u/Ucumu used) was a time of specialization and technological development. On the coast (traditional NW Coast - from the Alaskan Panhandle to far Northwest California) the earlier period's people had a subsistence strategy that was diverse and unspecialized, but focused in the littoral zone on shellfish, anadromous fish, and sea mammals as well as terrestrial plants and animals. By the end of this time period, NW coast people were specialized fisher-gatherers and sea-mammal hunters.
Subsistence technologies also witnessed significant change. By the end of the period, technologies for deep sea fishing were in place (boats, fishing tackle, and specialized tools) as were methods of mass collection of salmonids by damming rivers, setting traps in estuaries and using nets.
Settlements were small but there is evidence of nucleated villages as early as 3000 BC. By 1000 BC there are large coastal villages with many large houses.
Trade is evident early with obsidian moving west and shells and she'll beads moving east. At the end of the period of interest, there is an abundance of materials traded in all directions, including copper from the north and abalone, dentalium, and olivella shells. there is also evidence of social stratification indicated by the relative abundance of grave goods.
Moving east of the Mountains to the Plateau, the beginning of the time period sees the development of the first houses at a couple of sites on the Snake And Columbia Rivers but most believe that subsistance, and thus settlement, was dominated by foraging by highly mobile people. Plateau people were thought to have been developing a focus on anadromous fish but no evidence of real specialization is apparent. Sites that have good faunal preservation show a wide variety of upland species, dominated by large land mammals like deer, elk and bighorn sheep. Small mammals are present as well. As are fish and freshwater mussel.
By the 1000 BC, the settlement and subsistence pattern known as the Plateau Pattern is in place. The hallmark of the Plateau Pattern is the winter village of many pithouses, usually adjacent to a river or perennial stream. Along with the winter village there were a variety of seasonally occupied secondary villages/camps. These sites were located to ease access to seasonally available resources such as camas, bitterroot and balsamroot (root crops), seeds and berries, land mammals and fish. They used a true "seasonal-round" settlement system moving several times per year.
Trade is evident throughout the period 3000-1000BC but intensifies later in the period with many pithouse villages showing evidence of caches of unmodified shell from the coast.
Around 1000 BC or very shortly after (we don't really know) natives of the plateau developed bow and arrow technology.
Edit: Sources: K. Ames and H. Maschner, Peoples of the Northwest Coast, their Archaeology and Prehistory. 1999, Thames and Hudson. London.
R.G. Matson and G. Coupland, The Prehistory of the Northwest Coast, 1995. Academic Press, London
Lee Lyman, Prehistory of the Oregon Coast, 1991, Academic Press
William Sturtevant, Ed. Handbook of North American Indians vol 12 The Plateau. 1998. Smithsonian Institution.