Second Monitor Issues

You haven't given much info here, but some common things to check:
* Does your laptop actually support dual screens? Some don't have the capability to do so; you can use the external or the internal, but not both. (Others may support it, but have drastically lower performance; I've used one that could easily run CoH on the internal 1400x900 LCD, but if you connected an external 1920x1080 HDTV the performance would tank to unplayable levels).

* Do you have reasonably current drivers for your video card? The default drivers that come with many OSs may do OK for simple use, but not support dual monitors, etc.

* Have you enabled your OS's dual-screen output? Frequently on a laptop this would be toggled by Fn + a function key, sometimes labled "LCD/CRT" or having a picture of a monitor. Usually this will toggle through three modes by default; built-in screen only, presentation mode with the external screen cloned from the internal, external screen only. Setting to have internal and external as separate displays may require advanced settings.

* Have you configured your driver and OS to have the sort of dual-screen arrangement you want? In some versions of Windows for instance, there are multiple ways to set them up.

* Have you verified that the external monitor is on and set to HDMI input? Some don't auto-detect well, you may need to change it from "Auto" to "HDMI" or some such.

* Have you checked in the laptop's BIOS to make sure HDMI output is enabled?

* Is the laptop plugged into working wall power? Some laptops don't talk to some of their external ports if on battery power.

* Once everything is set and connected, have you rebooted with it all connected and turned on? Some laptops check for an external connection on boot, and if not present disable the port to save power.