In the most basic sense, cocktails are about making overpowering alcohol more palatable, frequently by adding water, either as water or as a juice or a soda, such as in a vodka-cranberry. A slightly more advanced aspect is making it easier to enjoy the full range of flavours in a base ingredient, for instance by sweetening and then souring it, as seen in the Whiskey Sour, the Caipirinha, etc.
The most advanced, and difficult aspect of mixology is combining ingredients to achieve synergy of flavour: a great cocktail creates overall flavours that are almost impossible to detect in the individual ingredients, such as with the Martini and Sazerac.
Ingredients matter, thus. Freshly squeezed juices. Decent liquors and liqueurs. Fresh, cold ice. Fresh fruit, herbs and condiments. The right glassware. Attractive, logical, minimal garnishes. If you have these items, you won’t go far wrong.