The wallpaper above my shower is peeling. What is the proper way to repair this? I've never wallpapered before!

Carefully peel back the paper and apply a thin coat of paste/adhesive to the back, then brush the paper flat with a damp cloth firmly in the direction of the edge.
If there is any patching to do always remember that a torn edge is not as noticable as a straight cut, it blends in with any pattern.
Make sure the surfaces are dry before you start and give the paper time to dry before using the shower as the steam and condensation will make your repair peel again.

I wallpapered my bathroom about 5 yrs. ago and it is holding up beautifully. Applied a wall sealer then the pre-pasted paper to all the walls except for above the shower. On that wall I mixed some carpenters glue with a bit of water and painted it on then the wallpaper while it was still wet/tacky. No buckles, peeling, etc.

Personally, I'd say steam it off
and use paint instead.

I recently steamed off the wallpaper
in my kitchen and am happy about it!

Painter's tip:

After repairing the peeled wallpaper, take a throw-away brush and apply a liberal coating of 5% silicone solution (available at most paint stores) to all paper within close proximity to the shower. This will stop the moisture from contacting the paper itself and prevent a reoccurrence of the problem for years and years.