On a continental scale, there wasn't a single population crash. It was a combination of several events and circumstances over the course of centuries: epidemics, warfare, slave raids, brutal working conditions, forced removals, etc. However, when people bring this topic up, they're generally referring to a handful of specific events, the main one being the epidemic that struck the eastern coast of North America in the latter half of the 1610s.

This is the epidemic that caused severe devastation eastern Massachusetts just prior to the arrival of the Plymouth colonists. The exact identity of the disease responsible is unknown. The current front runner is leptospirosis. If it's leptospirosis, it could be a local disease but it could also have been brought by Europeans - English slavers were making forays into the area at the time. It struck mainly along the coast at as far south as Virginia, leaving inland regions untouched. But while individual cases were widespread, the disease was not as equally devastating everywhere. Eastern Massachusetts was hit hardest, with whole villages being wiped out. In Rhode Island, the situation wasn't nearly as brutal, but still significant. This disparity in population loss is what prompted the Wampanoag Confederacy in eastern Massachusetts to allow the Plymouth colonists to settle among them. The Wampanoag feared that the Narragansett of Rhode Island would take advantage of their current weakened state, and a European ally with access to European goods would help boost their ability to resist a hypothetical Narrangsett offensive. By the time you get to the Pequot in Connecticut, very little of the population died there. The Pequots still had a population of 16,000 or so when the next big epidemic - the smallpox outbreak in the early 1630s - hit. By the time of the Pequot War in 1637, the Pequots were down to about 3000 people - and almost extinct after the war.

On the Plains, archaeological evidence indicate that the Mandan (one of the major sedentary cultures on the northern Missouri River) had a population between 15-20,000 prior to European Contact. After the smallpox epidemic in the 1770s, this was reduced to about 2,000. After the smallpox epidemic in 1837, fewer than 200 Mandan survived. In contrast, over this same time period, the Lakota and Dakota (among others) had abandoned sedentary living and adopted a nomadic horse culture. They were hit by the epidemics too, but generally suffered less and were able to expand westward from Minnesota to the Black Hills. For the Lakota in particular, between 1800 and 1880, they're population doubled from 8,000 to 16,000. In general, nomadic people fared a better against diseases than their sedentary neighbors, since they had fewer people in close quarters for the disease to spread rapidly among.

For this answer I will be jumping back and forth from previous answers I've written to similar questions. Feel free to check out the Frequently Asked Questions section for other answers, and my AskHistorians profile, for more information as well. Here we go...

First, the 90-99%% mortality figure that we commonly hear is a generalization for the entire Americas and reflects excess mortality due to a wide variety of factors after contact, not just infectious disease. The 90-99% figure that dominates the popular discourse has its foundation in the study of mortality in conquest-period Mexico. Several terrible epidemics struck the population of greater Mexico (estimated at ~22 million at contact) in quick succession. Roughly 8 million died in the 1520 smallpox epidemic, followed closely by the 1545 and 1576 cocoliztli epidemics where ~12-15 million and ~2 million perished, respectively (Acuna-Soto et al., 2002). After these epidemics and other demographic insults, the population in Mexico hit its nadir (lowest point) by 1600 before slowly beginning to recover.

Though the data from Mexico represents a great work of historic demography, the mortality figures from one specific place and time have been uncritically applied across the New World. Two key factors are commonly omitted when transferring the 90-99% mortality seen in Mexico to the greater Americas: (1) the 90-99% figure represents all excess mortality after contact (including the impact of warfare, famine, slavery, etc. with disease totals), and (2) disease mortality in Mexico was highest in densely populated urban centers where epidemics spread by rapidly among a population directly exposed to large numbers of Spanish colonists. Very few locations in North America mimic these ecological conditions, making the application of demographic patterns witnessed in one specific location inappropriate for generalization to the entire New World.

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The MCA (medieval climatic anomaly) was partly responsible for both the population increase in Europe and the decrease in the Americas. This did not happen all at once but from around 950AD-1200AD. Nearly every advanced Native American civilization went through some sort of a crash or decline during this time. Cahokia in the Midwest is an example of this, but other areas had collapses as well. The Anasazi in the SW, as well as the Salish tribes up in the NW. The MCA is not the sole reason or even the primary one for many of these peoples, but can definitely be pointed to as a factor. The native Americans; contrary to contemporary beliefs were not environmentally sound and created a lot of these problems themselves with over farming and unsustainable growth.

Sources: 1491 by Charles C. Mann

Ancient North America by Brian Fagan