First you need to send an application [1] to the Swedish transport agency (Transportstyrelsen) and have it approved at least 30 days before the release of the balloon (the application alone will set you back about $200 US).
There are a bunch of regulations for the aircraft as well [2], radar visibility related for example. And for the time of the release; at most 2/8ths of the sky can be covered by clouds, visibility must be at least 8km. It's illegal if these conditions aren't met.
If you have a camera on board, you will have to get all footage vetted by the military to make sure you haven't photographed any secret installations or similar. As best I could find out, you send them the complete raw footage of everything and they give you back whatever's cleared by them. (I didn't ask official questions regarding this, so it may be I misinterpreted the information I did find.)
[1] http://www.transportstyrelsen.se/sv/Luftfart/Flygplatser-och... [2] http://www.transportstyrelsen.se/Global/Luftfart/Flygtrafik/...