There are lots of different ways to do it. A quick way would be to use the polygon lasso tool and click a path all the way around your silhouette. Once your path/selection is complete just copy and paste it into a new layer or new document. A slow way would be to use the eraser tool to erase everything around your silhouette. hope that helps.
You can use the "magic wand" feature, and cut it carefully around it. You will need to paste it into the image like Red said, as a new layer. If the picture that you are cutting from is on a light background, you can blend away the light edges with a eraser and the colour of your ground in which you are pasting it to. I find that if I can blend it into the same colour, it'll not look as "ovious" as a regular cut.
If you need help, feel free to drop me a PM. I just started working with Adobe, but I have a Wacom pad that has more control over smaller areas, than a regular mouse.