You need to fix the leak, fix the ceiling and then apply a stain block to prevent the stain (Tannin's) from coming back through the paper and paint.
Images help us give good advice on these situations but if you have never hung wallpaper, papering a ceiling is not the best place to start as a first attempt and getting a guy in would be a cheaper option.
But, if you want to 'have a go' you have several choices... You can either, dampen the hanging paper and leave it to soak for 5-10 mins if its not dry/brittle and try sticking it back with some standard wallpaper paste, failing that you could attempt removing a strip and trying to match in but to be honest if the ceiling has been painted it will be a road to disaster, especially if its away from the wall i.e. its the second length etc in from the wall, or you can remove all the wallpaper, bear in mind it could be an absolute nightmare to remove in places but once you start you just have to plug away at it, then you will have to either repair any damage found i.e. cracks, scraper digs etc, if its chaulky seal it with a pva glue or size and either line it with some grade 1000,1200 lining paper or if its really rough use a blown vinyl fresco type paper.