1. If you haven't done so already, turn the computer off.
2. Now turn it back on and depending how it is set-up, you should get a "beep" and may get some writing on the screen. Is this happening?
Note: some manufacturers just provide a "splash" screen, but we need to know if this part of the process is happening.
3. If you are not getting any screen at this time, turn the computer back off again.
4. If there was NO BEEP, the rest of this does not apply for now, so post back please.
5. Depends on whether the computer is under warranty or not. If NOT, remove the left hand cover as you face the machine. Now look for the connection the monitor uses. If this is integrated into the large circuit board that everything else connects to, there is little more you can do at this time.
If however it is a separate card plugged into a socket, you should remove the single retaining screw and gently remove the card. Try to avoid touching any of the connections along the bottom, but make sure they are all clean. Now replace the card into it's socket by giving it a firm push. Make sure it is fully seated back into the socket and replace the screw. If you can't replace the screw, you have done something wrong, so take a close look and repeat the procedure.
Sometimes, just the re-seating of the graphics card can be enough to solve problems like this.
Please post back with how you get on.