The heart of Mises' argument is that
1. There are no prices for the means of production under Socialism. [Obvious].
2. With no prices for means of production, they will be wasted. [Deep stuff, which we will go into a bit more in this humble article].
Let's look a bit more at how things work in a free market. Mr A is a successful businessman. He comes up with a great new idea, say laptops that glow in the dark. He does his market research, and finds that customers will pay an extra 50 bucks for a glow-in-the-dark laptop. [Yes, I am making this all up, and I'm going to make up all the prices involved, too.]
So he opens up his catalogue of Shines in the Dark Plastics, and he is very surprised to find that that stuff is pricey. In fact, it will cost him 60 bucks per laptop to coat them. He will not make any more money on those planned shine-in-the-dark laptops, in fact he will lose 10 bucks per laptop.
Not wanting his dream of great fortune to go up in smoke, he calls up Mr B, CEO of Shines in the Dark Plastics, and asks him for a discount. "I can't do it," says Mr B. Mr C is buying up all my stuff like there's no tomorrow, and paying full price. So he's going to get it all, unless you outbid him. I certainly can't give you a discount."
Intrigued at this point, Mr A calls up Mr C. "How can you possibly afford to pay B's outrageous prices for his Shine in the Dark Plastic™?"
"Simple," says C. "I make glow in the dark skeletons, and people love them. Every Halloween they pay a cool hundred bucks per skeleton. Sixty bucks for the plastic, a few more for other expenses, and I make about twenty dollars a skeleton. And it's become a tradition to buy a new skeleton every year. I'm a rich man."
Mr A hangs up indignantly, and decides to move to a Socialist country, where he thinks he might have better luck. Comrade Marx, leader of the country, welcomes the talented and experienced Mr A with open arms, and appoints him head of a newly opened laptop factory, with carte blanche to do as he pleases.
"This is more like it," says Mr A, rubbing his hands together. "To each according to his needs. Well, my factory needs some Glow in the Dark Plastic, and Comrade Plastic, who runs the factory that makes the stuff, has agreed to give me as much as I want."
The glow-in-the-dark laptops hit the shelves. People are pretty pleased with the cute little novelty laptops, which sell at a very reasonable price, until Halloween comes around. They go to their shops to get some skeletons, but there are none on the shelves. When word leaks out about what happened, that all the plastic went to coating their laptops, they go home disappointed, cursing their stupid laptops, and look yearningly over the border at Freemarketville's homes, all gloriously decorated with shiny, scary, skeletons.
You see what happened. The free market, with its price system, made sure that the shiny plastic was used for what people wanted most. The Socialist country, by contrast, had no clue about how to use its supply of glow-in-the-dark plastic.
Of course, this story is not just about novelty plastic. The exact same thing will happen to all the resources at the Socialist country's disposal. Lacking a price system, they will have absolutely no idea how best to use them. Result: Suffering for all.