Today we can look at alchemy and say it was pseudo-science, occultism, and just plain crazy. We have images of an unkempt train spotter (or should that be coach spotter?) in the medieval equivalent of an anorak hunched over his heated retort adding foaming chemicals to something nameless at the bottom. We know it was crazy because gold is an element and you can not change one element to another by chemical means. Copper will always be copper, and to change it you need the type of energy found in the heart of dying stars.
To understand alchemy it is necessary to understand a little about the cultural context and the knowledge of that era. Well before they learned how to make metal from ores, our ancestors probably discovered naturally occurring gold, the native American civilizations who never transitioned from the stone age certainly did. Some time in the late neolithic (stone age) our ancestors discovered how to use heat and chemicals to treat stones "ores" containing metallic salts and oxides to turn the compounds into metal. The metals created from this were soft ones like copper and tin. South Americans made sewing needles out of gold and Ötzi the Austrian Iceman carried a copper axe, so these primitive metals were usable.
Our ancestors were as smart as we are, and experimented and learned. After a while they discovered that if they mixed soft metals together they could make harder metals and the bronze age was born. Later came the discovery of iron, and how to mix iron with other chemicals to make harder forms of iron and eventually steel.
Meanwhile gold hadn't been forgotten, it was then as it is now a highly desirable and precious metal. Enter the alchemist who reasoned "If mixing different metals makes hard alloys, and I know that some ores make harder versions of the original metals, presumably because ores already contain more than one type of metal, and gold is soft, then if I can remove the impurities from other metals I should end up with gold and be rich." These alchemists didn't have our knowledge of elements, so the logic was entirely reasonable for that age. It was further enhanced by the "four elements" theory of antiquity, this held that all physical objects were made from different combinations of only 4 elements.
With the knowledge of the time, the alchemist's theory wasn't actually too bad. Mixtures are hard, I want soft, so I'll un-mix. Unfortunately the theory was flawed, and they began casting around for better theories, these theories led them further and further down unproductive roads, and further from what we now regard as the truth. Eventually starting with people like Robert Boyle and his book The Sceptical Chymist, the experimental and more logical aspects of alchemy became chemistry while the more bizarre elements wandered off to become a true pseudoscience. Robert Boyle himself is largely regarded as having his roots in alchemy, yet his book is regarded as the start of modern chemistry and chemistry as distinct from alchemy dates from its publication in 1661.
For over two thousand years (and possibly several thousand years, depending on when Egyptian alchemy began) alchemists slaved away in secret on their impossible mission, and in the meantime made a large number of important discoveries and laid the basis of modern inorganic chemistry including a lot of the laboratory equipment that early modern chemists used, in China the alchemists searched for and made medicinal discoveries some of which are in use today.
We should salute these explorers as early scientists and while we must never forget their excesses we need to balance these against the benefits they bought us.
Of course the final irony is that even if they had succeeded and found how to make virtually unlimited quantities of gold, rather than becoming incredibly rich they would have just devalued the value of gold and we'd be using it to roof houses. A similar thing happened in the time of the conquistadors when they brought large amounts of Aztec gold back to Spain and invented inflation.