How can I organize my linen closet?

Shelving and bins after everything is taken out. Throw or give away things that you don't need. Shelve the larger stuff by folding and putting together similar things and bin the smaller items.

If you have sheet sets, fold each sheet, and 1 of the pillow cases then place into the second pillow case and fold the end over, that will keep all your sets together and use a little less space, also any towels/face cloths that are old, have holes etc toss them or use for rags etc. The remaining towels and face cloths instead of folding, fold in half then roll them up, and get baskets or fancy up some boxes and stand the rolled up linens in them, then the boxes/baskets can be left standing upright or put on their side

Any blankets/curtains or items that you only use in the winter, or colder season, you can get bags to put linnens and clothes etc then vacuum the air out and it makes them way smaller, then you can change out summer things for winter things and have lots more space

First, only keep linens and the like in there. Weed out what you don’t need or use. 3 sets of bedding is more than enough and one should be on the bed. So bed linens should take up one shelf, towels on a second shelf. Then I’d do pull out plastic shoe drawers for small items (like extra soaps, cosmetics, etc) on a third shelf and you can stack them, as well. extra blankets and pillows can go in large wicker baskets on the floor. And you still have one shelf I haven’t used... ;-)