Dusty soil

I have this really annoying patch of dusty dry soil and I've been trying to fix it by adding organic mat. dead leaves and stalks of other plants. all of them end up drying out and then blowing around and not accomplishing anything. Any recommendations?

Try building a hugelkultur or sheet mulch/lasagne gardening beds, or growing stuff that likes sandy depleted soil

"all of them end up drying out and then blowing around and not accomplishing anything."

try covering your mulch with chicken wire weighted down on the edges with rocks. or you could pile old branches over the mulch materials. if you try the branches, use the crookedest ones you can find, because the spaces under the branches act as natural leaf traps in the fall. you're looking to make a small brush pile, not just use several straight branches in an attempt to hold the mulch down. the brush pile will also serve as bad weather shelter and home to various small critters, many of which are garden allies.

another idea - cover the area with straw bales, then grow plants in the bales. google straw bale gardening for details.

-Build a compost heap on the spot
Over time, any leachate from the heap will add fertility to the spot.  As the heap is turned, soil and compost will be blended.  When the compost is ready, haul away what you need, leave some to amend that spot.

-Gley
Look it up.  This serves as a barrier to keep moisture and nutrients contained.

-Hugelkulture
As a nutrient and moisture trap, this method is hard to beat

-Build
Since nothing is growing in that spot, seems to be a fine place for a shed, chicken coop, campfire pit.