Firstly you need an air gap to stop the sound leaking out by 'wobbling' the outside wall. You can do this by 'standing off' sound insulating plaster board from the outside walls to a gap of about 6"". Build a frame to fix the plaster board on and minimise the number of connections to the outside wall again to minimize the 'Wobbling' problem. Fill the gap with insulation, almost all wall insulation has its sound proof rating on it, I found the cheaper soft-roll insulation, rather than the hard slab type insulation, was easier to fit.
if you are really serious you then need to build an [url=http://en.wikipedia.org/wiki/Anechoic_chamber]anechoic chamber[/url], have a look at the link, this can be done with egg cartons on the wall as an approximation, but the closer you get to the cavities/spikes on the wall (shown in the link) the better the sound absorption properties of the wall itself, will be.
Alternative my wife suggest putting the shed in someone else's garden :-)
DIY how to tutorial projects and guides - Did you know we have a DIY Projects section? Well, if no, then we certainly do! Within this area of our site have literally hundreds of how-to guides and tutorials that cover a huge range of home improvement tasks. Each page also comes with pictures and a video to make completing those jobs even easier!