go in your ModWarfare folder : C:\Program Files (x86)\Activision\Call of Duty 4 - Modern Warfare\Mods\ModWarfare
there create a folder named demos : C:\Program Files (x86)\Activision\Call of Duty 4 - Modern Warfare\Mods\ModWarfare\demos

your demo are there : C:\Users\username\AppData\Local\VirtualStore\Program Files (x86)\Activision\Call of Duty 4 - Modern Warfare\main\demos OR C:\Program Files (x86)\Activision\Call of Duty 4 - Modern Warfare\main\demos

copy your demo into C:\Program Files (x86)\Activision\Call of Duty 4 - Modern Warfare\Mods\ModWarfare\demos

start your game
start ModWarfare mod
open console and type /demo demoname

fh tuto01

for mac user see there : http://fearless-assassins.com/tutorials/article/255-mac-os-x-cod4-demo-management/