Exchanges work in a very simple way. Here's an example:
I want to buy a lollipop in this price. (say $1) then a dude wants to sell his lollipop for $1. The exchange will act as a medium between us to process the transaction and in return, the exchange will charge fees as the "facilitator" of the deal that occurred between us.

Hope that that isn't hard to understand.

In that example the fee of the exchange must be some part of lollipop, but in that way the deal is not correct, because the object of the deal is lollipop, not the part of it. So i thing that i not a good example.