Most people use paint it seems. Others use Gimp, some use Photoshop, etc.
Open paint, open image, crop image to what you want and the area surrounding. DO NOT RESIZE THE IMAGE
Grab the pencil, draw in the border using black and make sure it's fully enclosed either to neighbor borders or water on all sides.
Grab the color sampling tool and sample a color your neighbors are not from the rest of the map.
Switch to paint bucket, and fill in the inside of your border with that color.
Grab the text tool and write your name on your claim.
When you're done it should look like what others have been posting.
Host the image on imgur or something other site.
Use the spoiler feature so the page isn't filled with images, and put your image link in the spoiler.
Write something nice like 'Oh please masters of the map who are so good as to give me land, may I have this claim?'