Suppose somebody develops a new language, with totally new characters. And a font for the same has to be created. How does one do that?
Creating a customized language font is not at all different from creating a standard font, as long as a standard keyboard can be used to write it:
Ad DA01 mentions, you can start by drawing your font and digitizing it using a tablet or re-drawing your curves with a scanner and software of your choice. Then you can use a program to convert your characters into a font.
ILoveTypography has a nice article on this: http://ilovetypography.com/2007/10/22/so-you-want-to-create-a-font-part-1/ There you can find a list of alternatives, methods and suggestions (there is also a part 2).
If your font has nothing to do with the current alphabets, then you will have to either create a new input hardware / software or use your language in a different way.