There are two issues we all have to deal with. The first is getting organized. The second is staying organized!
Currently I am tying up a box of flies to donate to TU. There are 14 different patterns in the box. I only have the materials out on my tying desk for one fly at a time. When I finish up the pattern, everything is put away before I get the materials out for the next pattern.
I keep the materials that I use like hooks, dubbing, hackle, etc in tackle boxes so I can grab and go.
My extra materials go into cabinets and bins for long term storage.
Gary Borger has the ultimate storage system since he knew the owners of Weber Fly Tying Company in Stevens Point, Wi which is 20 miles south of us. When they went out of business he bought some of the custom made furniture = storage chests and drawers they had for materials and hackle. It is all labeled with slide out drawers that hold the materials.
A site devoted to name puns- literally hundreds of pun names
"Weber entered the tackle business here in 1920, and his company made Stevens Point "the fly tackle capital of America." His 1950 obituary in the Journal said, "Mr. Weber and his associates, backed by practical fly fishing experience and an authentic knowledge of American conditions, introduced many innovations, promoting the value of these changes in nationwide demonstrations and instructions."
It all depends on how many flies you tie I suppose. For myself my tying has been condensed down to about a dozen patterns and I now tie perhaps 50-60 flies a year, I used to tie semi-professionally until it became uneconomical to continue. All my tying materials are in wooden boxes or the wooden drawers of my tying desk, I'm moving away from plastics/synthetics in my life.