Well Liz, as no one tried to answer your question, I'll give it a go. (Any help will be appreciated here!)
First of all when the trees are gut down, they are sent through to the saw mill where they are sawn into various sections for use of furniture etc. The rest of the off-cutts are then processed into a very fine mixture called "Pulp" (the same thing when you add water to paper) It is then tried out onto huge rollers and flatten to form your specified paper thickness (e.g. cardboard, paper etc.) This is then all rolled up onto huge rollers and then distributed to the various paper companies like your press (newspapers etc) Hope this was of some help. Best of luck trying to explain it to you child!
Reg007 is very close, but often when it is produced commercially the pulp, or slurry, is poured onto a very fast moving blanket or mesh, and another one is laid on top. The 2 blankets are then squeezed together using rollers, to remove much of the water, and the resulting mush is dried to create the paper.
in addition, to make paper easier to print or write on a proportion of kaolin clay is added. this is a very white, fine and smooth mineral which fills the gaps in the paper. it is also why wet paper gives out a white liquid when squeezed, and why thicker paper is more expensive.