Ever since elementary school, whenever learning about Native Americans & their history (a subject I enjoyed greatly), the conversion always referenced the percentage of NAs (Native Americans) killed by European colonists as upwards of 90%. Every single time this number is referenced I remember thinking to myself "How in the BLOODY HELL can ANYONE claim to know the total number of NA people killed down to the bloody percentage!?". My reasoning for this does not come from a place of vitriol; I cannot begin to fathom the amount pain endured by these innocent people for such senseless reasons. Still, seeing as how in the modern world, academics still constantly argue over the number of deaths that occurred during WWI, WWII, Vietnam, Chinese Cultural Revolution, Stalin's industrialization efforts, etc... for good reason, it seems outrageous that people can claim to know the percentage killed of a whole population over a span of centuries across an entire continent whether it was as low as 10% or as high as 95%.
Where did this 90% number come from, what source/report/paper/survey/whatever is everybody referencing? Is there a source? If I were to put myself in the shoes of a 19th century historian in search of the number of NAs killed since Columbus' arrival, I do not know where to even begin. How could Europeans keep detailed accounts of the number of all the natives they encountered in their travels? Why would they? Even if every conquistador did, how is that an objective reference frame considering the untold number of NAs scattered across the TWO-THOUSAND mile wide continental United States at the time?
You are correct to be dubious of these percentages, since the population numbers of pre-contact native American populations were so poorly documented. The key to arriving at this percentage is to take a close look at a much smaller area and extrapolating the hard numbers for a carefully selected and better documented area over a much wider (continent wide) area.
The first person to do this was Bartolome de Las Casas. He wrote several books on this topic from the 1520s through the 1560s and was an important reformer of Spain's relations with the natives. The best place to start with an in depth look at Las Casas work is his book "A Short Account of the Destruction of the Indes", which was published in 1552. Nigel Griffin published an English translation in 1999. Warning, this book gave rise to the Black Legend of the brutality of Spanish conquistadors. Protestants liked this, but Catholics hated it. Bartolome de Las Casas was also dismissed, out of hand until rather recently (after 1970) since he was deemed a "High Counter" that over estimated the population of Native Americans at the time of contact with the Spanish. As more archaeological research is done in the Americas, the pendulum has swung more towards the way the High Counters see things. This is detailed in Charles Mann's book "1491". However, Bartolome de Las Casas has also been under attack for one of the key parts of his reforms of Spanish New World colonies. Las Casas advocated importing African slaves to provide the labor the Spanish needed to make their colonies economically viable. If you work at a University that has a strong "Black Lives Matter" or a strong African American Studies department you will get into big trouble if you mention Bartolome de Las Casas to much. He was always and still is a very controversial figure.
Among the earliest of the modern High Counter historians that look into this issue are Sherburne Cook and Woodrow Borah. Their seminal work is "Essays in Population History" that was published in three volumes between 1971 and 1979. This book was the first major scholarly work that looked into the data of the biological causes of the dramatic crash in post contact Native American population. They did not harp on the human rights violations of Spanish conquistadors, but looked real hard at the data on the effects of diseases killing native Americans.
Sherburne Cook was a professor at the University of California Berkley. He published two smaller books on this topic that looked closely at much smaller areas. Baja California in 1935 and the Central Mexican Highlands in 1948. He worked with the old documents left behind by Spanish missionaries. His 1948 book was important, because it cast new light on the effects of small pox on the collapse of the Mexica Triple Alliance (Aztecs). Cook's work was not well received in 1948 and he was dismissed as being a "high counter". He kept plugging away though, and his most important work, "Essays in Population History" has swung the pendulum closer to the high counters way of looking at this question.