For a more advanced technique, you may need sugar pulling gloves. Take the hard crack sugar, after the additions are made, and pour it onto a Silpat over a heat protective surface. I like to use a thick cutting board just in case the counter isn't quite sturdy enough. Allow the liquid to cool enough that you can start to pull the edges inward. It will be like a very thick, very hot gel, that solidifies as you work. Continue pulling the edges inward and letting it cool, until you can remove the entire pool of sugar. Now pull the sugar out and twist it back onto itself. Continue pulling, twisting, wrapping, tucking, and bringing the mass back together. This will change its color and texture considerably. The air will create a popping sound in the sugar and you will start to see a shine. While still pliable, pull a length out and roll it on your silpat to create an even diameter tube or coil. Then start coiling this upon itself tightly. Continue wrapping the circles around themselves until you have the diameter lollipop you want. Quickly place the stick into the coils and pull it aways from the center to create a gentle teardrop seal between the stick and the candy. Allow to cool completely lying on the board, so it won't sag during cooling. Now you have the very classic, very iconic, twisted lollipop.
For more daring candy makers, pour out some of your sugar and color differently, then wrap that around your initial coil to create that candy-striped appearance. And don't forget that you can add any kind of alcohol of flavoring to these candies as long as they are reduced to an extract state.