Go into your base and type /demorecord name
Where "name" is whatever you want to save the file as.
Then either type /demostop, or just step back out of the base.
In your city of heroes directory you'll find a folder called client_demos. Inside of that will be name.cohdemo. Your base is contained in that file. You can also play it back by making a shortcut to cityofheroes.exe -demoplay name, then press F2 to detach the camera and look around.
