I am try to use the Battlecraft program to custom make a map for Battlefield 1942. But each time I open the program I continue to recieve a message saying,

(I require the WGL_EXT_SWAP_CONTROL OpenGl to work)

What do I need to do fix this?

WGL_EXT_swap_control is the OpenGL extension under Windows to control the vsync behaviour of the SwapBuffers call.
Docs here:

If the application requires that extension to be present and doesn’t work without, that’s silly of the app developers, because this is not really a must-have feature to render double buffered.

The only things you can try are:

1.) Install/Update your graphics drivers.
Go to your graphics board vendor first, if there is nothing new, try the graphics chip vendor. If you don’t know who that is, look in the Control Panel -> Display settings. Most likely NVIDIA or ATI. If not one of those, good luck.

2.) Look for a Battlecraft patch which resolves/fixes this limitation.

But this extension seems to be very widely available :

collen, can you find your card in the list ?