G'day, just thought I'd add my 2 cents worth as I've been researching this for a while now with the aim of building my own back yard studio/jam room which I wanna be able to use 24/7 , so it'll need to be mega soundproofed.
Basically the biggest issue you're gonna have with a tin shed is the shed itself, it's gonna resonate and rattle and become a big speaker for all your neighbours to hear! Deadening this would be the first step before even commencing any type of building. The best thing to use would be a product called Dynamat - it's used in car stereos to deaden the body of the car to eliminate rattles etc but it's not cheap. Alternatively the easiest way I could think of would be with body deadener like they use on cars, you know, the black tar shit that lines the underbody and door panels etc. It's pretty cheap and easily available (Bunnings, paint or auto shops etc) and easy to apply, just need some big cheap paint brushes. It would possibly be worth using the adhesiveness of it to stick some shit to the tin to help absorb any sound that hits it aswell at this stage (insulation or dacron, the white foam shit inside speaker boxes would work well).
When constructing the room itself I would definitely be looking at limestone blocks rather than double brick, it'll be cheaper and more solid, thus absorbing more sound. Also due to the size of the blocks it's much easier to lay them than using small fiddly bricks (unless you've got bricklaying experience), if you can use a tape measure, string line and level you should be pretty right!
The basic rule when soundproofing is separation between different mediums... the more the sound has to go through the more it will be adsorbed and dispersed. The easiest way to achieve this is by doing what you were originally thinking, build a room inside the shed. This is where it becomes important not to attach any part of the new room to the shed itself because sound will travel through whatever you use to attach it and will end up rattling the shed as I mentioned before. The hardest part to soundproof will be the roof and you'll probably have to borrow Simons idea and load the roof up with foam, matresses, carpet etc.
Finally, something that most people don't even consider when converting sheds etc into usable rooms is termites. I'm a professional pest controller and have been to so many jobs where sheds are converted into granny flats, games rooms, teen retreats, offices etc. only for the termites to get into the walls and eat the stud framing away. If you use any timber make sure it's treated/structural grade and try to eliminate any timber-ground contact. If the shed is on 2x2 concrete slabs I would strongly advise lifting them and pouring a solid slab, if it's on a solid slab already be very aware of gaps (particularly around the edges) and expansion gaps as termites only need a 1.3mm gap to get through and LOVE seeking out cracks in concrete etc to see what's on the other side.
Good luck, hopefully it kicks arse!!
