In order to mud and tape the corners with new drywall you, you will need spackle, a sturdy ladder, and a putty knife. Scoop out a dollop of spackle (i.e. mud) with your putty knife. Place your putty knife where the ceiling and the wall meat. Spread the putty evenly, as you extend your arm left to right or right to left. Make sure that you apply putty all the way up to the corner.
Next, dip your putty knife into the spackle again, and rake it across the ceiling in a similar fashion. Lay the tape in the corner. Press the tape in the seam with the putty knife. Spackle over the tape. Make sure it is smooth, and it will reduce the amount of time you will have to spend sanding.