There are "auctions" every so often for the rights to a custom banner slot. After you win one of these auctions, you will have the option of uploading your customized banner art (140x342 *.png) to this slot and using it for your clan.
The costs are prohibitively high for a single player (several hundreds of thousands of gold) so most custom banners go to clans, rather than individuals.
I suppose you you could unpack and modify one of the game's default banners and edit it to your hearts content (I've never tried this, but I don't see why it wouldn't work). Only you would see the custom art, but it wouldn't cost you anything.