Take the amount of sugar from whatever recipe you are making, and spread a very thin layer of it into your pot.
Cook it over a medium-high heat, gently swirling the pot on occasion. Do not stir it at any point (remember, we do not want the sugar to crystalize or to start clumping before it is all melted). The sugar will dissolve, and for a short time it will resemble water. Then it will start turning amber in color. Be sure to swirl the pot so that the hot spots do not overcook those areas of the pot.
Once most of the sugar is amber in color (the edges may be a dark, reddish-brown), sprinkle another thin layer of sugar, and continue swirling the pot. The new sugar will melt quickly and start turning amber in color.
Once that last batch is fully melted in and mostly amber in color, add another thin layer of sugar, swirling and cooking until it mostly all amber in color. Continue adding thin layers of sugar and cooking until all the sugar is cooked. In the end, the entire mixture should be dark, reddish-brown, and it should be lightly smoking. Do not cook further or it will start to burn.
Remove the pot from 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.