Go into your Mount and Blade install directory and find the textures folder.
Common install location is C:\program files\Mount&Blade\Textures
If you want to edit your current in game banner you have to the .dds file it's stored in. All the files relating to banners have the name "banners_
- .dds" where
- is a through to f. MAKE A COPY! That's important if you screw up you'll need to revert to something.
Convert the .dds file containing your current banner with the program mentioned before.
To replace it you open the .jeg or what ever and past over the current banner with the one you want. Save then convert the new banner file back to a .dds with the same name as the original and replace it in the textures folder. It should now be changed in game.
I'll try to write a better guide with pictures etc in a bit