Where and how do people buy exotic animals?

Answer 1

Depending on the animal, they can get them from breeders or brokers. If you live in the US, you need to first check your state laws to see if the animal you desire to own is legal in your state. You can check that here: http://www.api4animals.org/b4a2_exotic_animals_summary.php

If the animal is legal to own in your state, then you still have to check with your county and local authorities, as many individual counties and municipalities ban the ownership of animals that are otherwise legal in the state.

If the animal is legal for you to own, then do a websearch for breeders or sellers of that animal in your area, such as:
"tiger breeders in MN" or "tigers for sale in MN"

Answer 2

There are also exotic animal auctions, the local one charges admission because a lot of people come just to see the animals.