This was before the availability of so many packaging options.... but I remember them being stored in the pantry, dried out mushrooms in mason jars.
You can easily dry them on a screen or in a fancier dehydrator. Mine is made by Presto - bought it a few years ago. It’s got all the bells and whistles. I just love it.
I mainly dry small homegrown paste tomatoes (Juliet or Valentine) which I then put in oil and spices and keep in the fridge. Beau eats them like candy. The dehydrator is also a great way to make jerky and a friend is obsessed with making fruit roll-ups, which don’t appeal to me in the least.
Presto Dehydrator: https://www.gopresto.com/product/presto-dehydro-digital-electric-food-dehydrator-06301
I bought mine on sale at Farm & Fleet, and had a $25 gift card, so it was well worth it. Presto is a Wisconsin company, too. On, Wisconsin! :)