Buying from the Public Market
How to buy from the public market is no problem at all (or at least, it shouldn't be. A quick recap: You put in the amount you want to buy, and click "Buy!"). The Public Market, as a consumer's resource, has a few advantages over the stores of the Imperium. One is that prices can be lower - some of the items are stolen, and some may just be extra. If the prices are higher than at the stores (and you should check), then buy it at the store. Another advantage is that you might be able to get an item there that stores are not stocking.
On the other hand, the Public Market has one large flaw - nothing is guarenteed. Nothing is guarenteed at the Public Market. You may pay for something, and never get it (You also may get something, and never have to pay for it). If you've checked out the Selling at the Public Market page, you'll see that you can try to "Swindle" customers (or yourself), decreasing the chances of a transaction by 20%.