Funnily enough I'm actually in the process of doing this with my shed right now. It's actually not that difficult or overly expensive depending on how you approach it. As others have said air gaps and vibration are the ones to watch out for.
As a bit of info on my particular approach, the way I've done mine is standard 90 x 35 pine framing, double plates top and bottom, and double studs every 4 feet at the sheet joins. Roof is zincalume with 50% overlap of very heavy duty sisalation. Outside walls are lined with the same sisalation also generously overlapped, then 7.5mm cement sheet nailed on. The inside is filled with R3.5 non-allergenic fibreglass batts, then 12.7mm mdf sheets are screwed (not nailed!) into the framing at one foot intervals. At every join for the framing, roofing beams and purlins, and MDF, I have used fairly substantial runs of the cheap $2 construction adhesive. Heaps of adhesive! This is not the complete solution obviously, but is part of the easiest way to help minimise noise transference. You can whack any part of the shed and all you'll hear is a dull thud, no vibration. So far the results are staggering, even without the roof insulation or inner lining done yet, amazing drops in temperature, and even though you'd think the echo from the wall mdf would be massive, it seems I have enough junk around that the sounds are completely deadened from outside. Down the track when I have everything in cupboards, there will be more echo as there will be large flat and hard surface areas, so I'll line the mdf with a thin but firm rubber surface.
Along with construction adhesive, expanding foam cans are your friend too! They are amazingly handy for filling arkward gaps and spaces.
Just remembered to add, another thing i'm doing that could prove very handy in your case, is i'm painting any moisture sensitive or exposed areas with brushable tar to seal and dampen vibrations. You would find this very handy to completely paint the inside of your shed before you line/insulate it as you can help bond vibration areas, and seal the gaps with it. It's a very cheap but effective method. And you don't have to be fussy at all about putting it on either, just slap it all over!
cheers,
Ian
It's rumoured that everytime someone buys a TB6560 based board, an engineer cries!