1. Download a map. (with borders)
2. Draw out the borders on your photo editing app (I use Photoshop). Draw the borders in black and keep the other stuff white.
3. Go to AppData/LocalLow/JoySparkGames/Ages of Conflict.
4. Put the image (needs to be .png) in the "Custom Maps" folder.
5. Open the game.
6. Look for the image.
7. When you've found the image, click "Play".
8. Start placing nations and fill out the nations' land.
9. (Optional) When you've finished, Start placing cities and recolouring the countries.
Save the scenario every few countries.

Here are some of my scenarios created using these steps.
https://steamproxy-script.pipiskins.com/sharedfiles/filedetails/?id=3247923924
https://steamproxy-script.pipiskins.com/sharedfiles/filedetails/?id=3296480900
https://steamproxy-script.pipiskins.com/sharedfiles/filedetails/?id=3294855260

Edit: Maximum size is 4,000,000 pixels. Check the aspect ratio before putting it into your game.