Read the readme! Pretty simple:

1) Unzip Easymod to where you installed the demo
eg C:\Program Files\Activision\Rome - Total War Demo\

2) Run Install Easymod.bat. Download xdelta.exe if instructed at the address provided (also in the readme if you want to copy/paste more easily).

3) To make your own battles, go to Data\world\maps\battle\custom\ and then either newmap for Trebia or newmap_tutorial for the tutorial. Take a look at the descr_battle.txt files and edit to your heart's content. Back up your work regularly, and if you get a crash just go back and try again.

4) To download other people's battles, just save the descr_battle.txt they provide in the appropriate directory (newmap or newmap_tutorial), overwriting the one there (back it up first if you want to keep your current one), then play!