Artillery fungus lives in mulch. It will get up into the air and attach to siding. It's called artillery fungus because it looks like bullets hit your house - it looks like a bunch of black dots all over.
To remove artillery fungus from siding, you have to physically scrape it off. You can do it with steel wool, very gently so you don't take the paint off. Or, you can treat artilery fungus with a mildicide like Jomax, and a pressure washer used very lightly so you don't harm the siding. Apply the mildicide to the fungus, let it sit for a good ten minutes or so, and then rinse it off.
Sometimes when you get the fungus off, you'll be left with a brown stain underneath. You can touch up the stained areas with an oil-based primer and then a top-coat paint that is as close to the siding color as you can find.
Of course, to address the root of the problem and keep the mulch from coming back, you'll have to change your mulch. If you want mulch that tends not to contain artillery fungus, don't use shredded wood. Use whole chips of bark. That tends to be much more successful than the shredded mulches.