In a medium-size pot, spread whatever amount of sugar is called for in the recipe you are making and use enough water to just cover the sugar. Generally, for 200 grams (1 cup) of sugar, use 58 grams (¼ cup) of water. The amount of water, however, does not need to be precise. You simply need enough to hydrate the sugar. If you use more water, it will just take longer to cook the mixture until you reach caramel stage.
If any sugar crystals get stuck to the side of the pot at any time during the cooking process, wet a pastry brush with water and slide it along the sides of the pot, without allowing the bottom of the pastry brush to submerge into the mixture.
With medium-high heat, let it cook, cook, cook. The water will evaporate, and the sugar will start cooking, eventually turning to a light amber color. Carefully swirl -- but do not stir (remember, we do not want the sugar to crystalize or to start clumping before it is all melted) -- the pot to move the mixture around. Some parts of the pot are hotter than others, which is why you will see the amber color in parts of the pot and clear liquid in other parts.
Once you get to the amber color you like (ideally, it should be dark, reddish-brown in color and lightly smoking), take the pot off the heat and use immediately. (By immediately, I mean immediately add any cream/butter or pour the caramel onto a heat proof surface right away. Keeping it in the hot pot will cause your caramel to continue to cook and likely burn.) If you are making Caramel Sauce, quickly, carefully and slowly mix your cream in. The caramel will bubble up like crazy, so just add a little at a time.
The entire process takes less than 10 minutes. Boom.