What did mammoths look like and how do you know this?

Answer 1

You can see the related link for a picture of a mammoth (pictures are worth a thousand words :) ).

We know this is what they looked like because the frozen carcasses of some species (complete with preserved hair) have been found in the Arctic Circle in both Asia and North America. Even without a full carcass, people can get a very good idea of what an animal looked like by examining fossil bones.

Answer 2

The more obvious answer is from the fossil register.

However, very recent (unfossilized) Mammouth tusks were the subject of trade in Siberia, and in Mongolia.

There is, even today, a very well known top-of-the-range fountain pen's brand that offers a limited edition of pens using mammouth tusk's ivory in the barrel pen's decoration.