Necessities

Let's start looking at some specific things that would need to be addressed immediately if money would disappear.  Here are the basics:

1. Food
2. Clothing
3. Shelter

About what you'd expect, eh?  Probably it will take at least an entire post for each one to get all the ideas out there. So let's start with food.

We can learn from history here if we look back at what happened during the French Revolution. One of the immediate effects of life in the Paris Commune was that all the food was used up pretty quickly, and nobody had planned for how to deal with the food distribution system collapsing. So starvation ensued, leading predictably to panic, finger-pointing, and frequent use of the guillotine.  It was not pretty, and the Revolution started to unravel immediately.

At one point farmers were offered script (revolutionary currency) in exchange for grain.  They were smart enough to realize that the stuff might shortly be worth nothing, and they held back their grain.  People starved, and grain rotted.

Here's what will get the problem solved quickly.  Organize a group of merchants such that everything a farmer could possibly need or want would be available through the group, then offer to let the farmer and any of his family or workers take whatever they might need from the merchants for a year in exchange for the farmer's crop.   The merchants can distribute the crops through their stores, or each merchant can trade it to other merchants. Next year they can negotiate a new agreement.  This largely solves the distribution problem by keeping the trades local, which saves fuel and keeps the goods fresher.

A variation with greater efficiency would be that merchants would merge, creating locally-supplied general stores. These would be replacing today's Big Box stores, which exist only because of the price advantages of scaling up.

Once again, we have eliminated all the bureaucracy and red tape of trying to ensure that everybody in the transaction gets an equal share down to the penny.  We just throw away the yardstick with the understanding that if you contribute what you can, you will get what you need.  We've also avoided the need for some kind of State distribution (and more bureaucracy) by keeping the agreements local.