Money is an abstract concept for the priority of resources. and the fundamental unit of trade. The only society which truly has no money is a society in which there is a total of no interaction between individuals. You might think of money as these bits of metal and paper, or as being abstractable only to the point where it's a number in a bank, but the laws of economics, finance and capitalism work with abstract money and can deal with any economy no matter what the fundamental unit of trade is - and there is always a fundamental unit of trade, even if it is purely abstract or never used.
Think about it this way. Even in a society where everything is trade between various goods and there is no "currency" and all trade is agreed by bartering. (Let's call them resource 1 2 and 3). Then there is a value ratio (between bounds) of resource 1 to resource 2, and between resource 2 and resource 3. The value ratio between resource 1 and 3 is determined by saying "swap all of your resource 1 to resource2, and swap as much of that to resource 3" - i.e. 1:3 = 1:2 * 2:3. This means that if the nessisary resource resource 3 becomes more scarce, the trading ratio between 1:3 and 2:3 goes up, and vice-versa. A little bit of looking might show you this is actually the law of supply-and-demand, but we're thinking in a hypothetical society that doesn't use currency! Furthermore, we can actually define an abstract currency for our model to be the number of resource 1 (in general any resource) that can be bought with some other resource.
If I have 1 unit of resource1 then by defintion I can trade this into 1 unit of resource1.
Value(resource1) = 1 Ms
If I have 1 unit of resource2 then I can trade this into 2:1 = 1/(1:2) units of resource1
Value(resource2) = 1 / (1:2) Ms
If I have 1 unit of resource3 then I can trade this into 2:1 units of resource2, and I can trade this into 3:2 units of resource1
Value(resource3) = 1 / (1:3) Ms
It's a bit abstract, but you'll see that despite the fact we're dealing in a society that trades with resources and never with money, we've managed to abstract a notion of money even though money is never "really" used in the society. If you want you can print tokens that represent Ms (we can even rename them, say, to "dollars" or "pounds").
There's two questions left though: If the relative value of 1 changes upwards or downwards with respect to every other resource, this can be seen (if you think about) to be deflation or inflation respectively. If the relative value of any other resource changes, it just changes the "price" of the resource.
So what was the point of looking at that? Well the point is simple. To show that even where you don't print cash, there's still money. Even in a society that doesn't THINK about cash, and simply trades resources, economics still applies and it's easy to contruct an abstract currency for which all of economic theory applies, even if that currency isn't actually used in the system.
So what does a resource-based economy actually involve? Basically it's about how the relative prices of things are set. There are three approaches:
1. All resources are dictated to be worth the same. This has a nasty side-effect that a loaf of bread "costs" the same as it's weight in flour. So there's no change in the baker's ability to obtain things via trade because his net "wealth" isn't changed by making bread. Indeed, if he has to go and make the fire that cooks it, he might be selling his life away. This is clearly unworkable.
2. All resources are dictated to be a fixed value either by public vote or by some committee in society. The committee in society approach is classic communism. The value of goods are set by the party and trading at other prices is illegal. This doesn't sound like a bad plan until you notice that there are hundreds or thousands of resources all with quite subtle interplay in the economy, and a the movement of prices by small amounts can cause rather large changes to the economy (and thus the ability of the people to eat and be merry). The voting system is interesting, but with people having other motives (i.e. there are more people eating bread in society than bakers) this will nearly always work against the producer.
3. The value of resources is determined by the most recent price traded, and there are no limits on what price a good can be traded for. This is classic capitalism. If resource B is in high demand, the value of resourceB goes up. If resourceA has a massive overproduction, the value of A falls.
If you want, you can think of money of the various resources as a quantitative measure of the resource's importance to society, and the reward for bringing more back. If you think of it like this, you'll understand that actually it doesn't matter HOW abundant resources are in society, always be priorities for resources, therefore trading, and there'll always be economists who think of things in terms of filthy lucre.