Wallpaper and Wallcoverings - wallpaper patch

I don't really have much experience to speak of when it comes to wallpapering. The situation I need advice on is removing a stained section of wallpaper where a urinal gasket had been seeping over time, and then patching in a replacement section. I do at least have the exact matching wallpaper to use for the patch. Here's a link to a photo of the stained wallpaper. http://i207.photobucket.com/albums/bb153/sgull1/wallpaper.jpg
The wallpaper is good quality commercial type wallpaper, not sure what type it would be specifically called; it seems to be paper and not the fabric type. I was thinking I would try to cut out a rectangular shaped section where the stain is, cut it down to the top of the cove base there I guess, and then patch in a new piece. How do I do this, what's the proper method to do such a decent patch that doesn't show much and isn't apparent to the average person not looking for it? Any comments/advice appreciated.

Addendum to post: The wallpaper is vinyl-backed paper. What's the best way to remove the old stuff, and especially, what's the proper adhesive to use for the new patch?