As a Canadian historian, I can answer better about the northern part of the continent, so I'll leave someone else to talk about the Southern US. Estimating numbers is pretty much impossible, too, because disease often spread ahead of European arrivals and because there's no written record to go off of. It's kind of a general question so I hope I'll point you in the right direction.

So, what parts of the continent were populated? Pretty much everywhere. Check out this map that demonstrates the names of First Nations in the areas where they traditionally lived.

However, we know that more dense communities were built up on the West Coast of Canada as well as around the Great Lakes, based on what kind of communities people lived in - the settled villages of the Great Lakes and the West Coast lend themselves to a denser population.

Around the Great Lakes, there were settled village communities who practiced "horticulture" - growing food in gardens without ploughs - and grew squash, corn, and beans especially. (Interestingly, these three plants' respective nutrient needs and way of growing makes them grow better when planted together!) These groups included the Iroquois and Huron, and you have likely heard about the style of life practice in longhouses there - this article by a McGill archaeologist talks about how those communities looked and functioned. The horticulture, as well as food storage methods used in the longhouses, let the communities get denser and bigger than elsewhere in the continent.

However, the West Coast was perhaps the most densely populated. British Columbia has over 34 indigenous languages and about 60 dialects are still spoken today, which should give you an idea of how many different communities were there. More permanent villages were constructed along the coast by the over 203 indigenous nations there.

To sum up, density depended on the kind of fishing and hunting you could do. Groups that had to move around to follow animal herds (ex, the Cree in the Prairies), groups that had to seasonally move to fish and hunt (ex, the Mi'kmaq on the East Coast), and groups that lived in areas which yielded less food per square km (ex, the Inuit in the Arctic) developed smaller community sizes and would meet up periodically instead of living in dense village formations like the ones on the Great Lakes and in coastal BC.