The idea is that when the slots stop spinning, you choose a row to collect the resources for (or suffer the consequences of in the case of the dragon spaces).
Each turn, you will likely collect one or more coins. You can either spend them at a merchant that appears in the same row, or you can bank them for spins later. If you spend them at a merchant, you can buy new slot spaces; they appear below the merchant's slot and will start showing up on future spins. The reason some items are blacked out at the merchant is because you cannot afford them with the coin you have collected that round. (The coins you have collected that round are shown on the left, and are only banked when you move to the next spin; that way, if you collect two 2-coin spaces for a total of four coins, and there are also two merchants, you can spend 3 coins at one merchant, and 1 coin at the other merchant if you want.)
There are two ways to get swords: Buy them straight out with coins, or forge them yourself with a furnace and metal. Buying them straight up is expensive, and require you to collect 6+ coins on a single row with a merchant. To get to that point, you need to have 2-coin and 3-coin slots land serendipitously, which can be rare. Forging them is slightly cheaper, because one furnace can turn any number of cheap metal slots into swords, but then those slots aren't useful for buying other things. To forge a sword, you need the slot wheels to land so that both a metal and a furnace space are on the same row.
The wizards are good for cleaning out less-valuable slot spaces. When the game starts, there are several blanks, and as you get further in the game, you might want to start destroying 1-coins to make your 2-coins and 3-coins more likely to come out. In the end game, wizards can save your hash by making everything but the swords and any remaining dragons less likely to appear.
It's hard to kill the dragon – even I cannot do it reliably, and I wrote the game. But once you get the hang of the mechanics, it is definitely do-able. You just have to find that sweet spot of not cluttering up your wheels too much, getting swords out as early as possible to start cleaning dragon slots, and trying to sneak in some score points in there as you go.
(Until you've slain the dragon at least once, I'd recommend not buying any score laurels. Focus on getting the strategy down for killing the dragon first.)