Depending on the pattern and color of the wallpaper, you may not be able to hide the failing joint. Check the drywall carefully for the reason for failure. It may be necessary to add a few screws at the failing seem if nails were used previously and have begun to 'pop' or pull out of the framing behind the drywall. I've often found previously applied paper tape fails when dryed out and it becomes brittle. Remove any nails that no longer hold properly as they will continue to 'pop' and create noticable bumps. Be certain your new screws just dimple the surface of the drywall without tearing through the outer paper.
Thorough and complete preparation of the work area will mean a much smoother project and finished wall. Every imperfection will be magnified by paint or wall paper.
If the tape is completely pulling off the seem or has dryed out and become brittle, consider removing it and sanding down the area to create or uncover the recessed area as when the drywall was new. You will need this trough to re-tape and apply 'mud' to a level even with the existing drywall and hide the seem.
Start with a 3-4" knife and lay a very thin layer of mud in the trough and compress it into the joint and any nail or screw holes you've made during repair. Quickly apply the tape starting at one end of the seem gently pressing the tape into the mud you just put down. (There are two types of tape available, one of a paper variety and one of a mesh fiber variety. I prefer the mesh myself as I've found it easier to work with when covered properly and less likely to slide as you're applying the first layer of mud over it). Use the edge of the knife to hold the tape firmly against the wall and tear it off against the knife (like you would tear a sheet of paper against a table edge). Smooth out any lumps or ridges immediately and allow to dry thoroughly.
I've found two of the biggest mistakes made by first time 'mudders' is applying a mud layer that is too thick with creates shrinkage with pits and splits and trying to finish the job too quickly and not waiting for the layers of mud to dry thoroughly. Then, when applying the next layer, you end up with half dry chucks of the previous layer stuck in your finished layers which only means more sanding and smoothing.
After you're certain this is thoroughly dry all the way through, sand any ridges being careful not to sand all the way through and damage the tape then lightly apply another thin layer of mud with a 6" knife which allows you to feather the edges out to become thinner and tranition to the level surface of the drywall. Apply a third layer with a 12" knife in the same maner.
One helpful tip to eliminate some sanding mess in an existing and finished home is to gently mist the new almost dry mud with a spray bottle and use a window cleaning rubber squeegee to make a smooth finish.
Good luck. This is dirty, messy work and is often worth hiring someone who will clean up when complete if it's a bigger job.
---Chris
