My basic caramel recipe is to cook white sugar over medium high heat in a pan. The sugar will begin to liquify and brown. Take the pot by the handle and swirl the sugar until it evenly browns.

This is pure caramelized sugar. From here you can take it several different ways.

Here is how I would make a sauce:

For a sauce, once it begins to smoke, lower the heat and add a tablespoon or two of butter. Once that is incorporated add a splash of cream and some salt. Some of the sugar will harden. Let it heat through and come together into a thick sauce. Off the heat, add vanilla.

Couple of tings here....once the sugar begins to smoke, it is burning and I toss it out. Secondly if you add butter to melted and browned sugar it will sizzle and bubble and be almost impossible to mix.
For camelized sugar, say to pour over a cake in threads or to line a flan dish, I do like The "pro" says and melt the sugar in a heavy pan until it's caramel color....but I remove it well before the smoke point.
For a sauce, I mix 1 cup white sugar, 1 cup brown sugar, 1 cup butter and 1 cup of heavy cream, cook slowly and stir, and continue to cook for 4 or 5 minutes after it starts to bubble. That's Ann T's recipe....and it's perfect!

If it is smoking heavily it is burnt, but taking it to that edge between "done" and "ok boys lets take it off the heat before we ruin it!" brings out the maximum flavor. Its a fine line to walk, for sure.