Materials for
Prepping Walls
Spackle (compound)
Fine-grit sandpaper
(100-120-grit Aluminum Oxide or Production)
Detergent and ammonia or tri-sodium phosphate (TSP)
Self-adhesive drywall tape
Primer or adhesive pad
Sizing or vinyl preparation liquid (for wallpapering)

Tools for Wallpapering
Steel tape measure
Plumb Bob or 48" Level
Water tray
Seam roller
Wallpaper smoothing brush
Razor knife with lots of blades
Broad knife
Large sponge
Bucket
Pencil
Ladders
Materials for Wallpapering
Wallpaper
Wallpaper paste (if needed)
Rags

Tips:
If you try to lay the first strip back down over the second, but it has dried too much to stick, simply apply more adhesive and smooth it down again.

If you can't peel back the first strip of paper from a corner because it's already dried, in order to get a clean, even seam, just overlap the second strip and gently cut through both pieces at the same time right in the corner - and hope neither strip shrinks enough to show a gap.
 
 Matching patterns as you go in and out of corners can be tricky, as corners are never straight or plumb. Be prepared to try more than once to get it right.
 
Door and Window Frames
1. When you reach a piece of trim, smooth down the paper against the trim  as best you can.
 
2. Use a pair of scissors to cut off most of what flops over the trim, leaving only about 2 inches to work with.
 
3. Where the trim makes a corner turn (for instance, going from vertical to horizontal),  make a diagonal cut in the paper, starting from where the paper touches the corner, and going out to the edge of the remaining inch or two. This will allow the paper to lay flatter.
 
4. Smooth down the paper again, and, using your trim knife and razor, cut the paper against the trim as you would against the ceiling or baseboard.
 
Tips:
Sometimes the next full-length strip after a window or a door does not quite  match up with the smaller strips above or below a window, or above a door.  You may have to "cheat" a little by lapping the strips over each other a bit. If that doesn't work, simply try to match the pattern at the most obvious place - eye level.
 
When papering next to trim or a molding that has lots of detail, make a little diagonal slit at every corner to allow the paper to lie flat. These kinds of fine details may require the use of a smaller, pointed razor-knife.

Corners
1. Use your trim knife to press the wallpaper into an inside corner and cut it with your razor, treating the paper just as though it were going against the ceiling or baseboard. 
 
2. Smooth down the whole strip, then peel it back from the corner a few inches.
 
3. Draw a new plumb line on the adjacent wall with your carpenter's level, measuring out from the corner the width - minus a half inch or so - of a piece of wallpaper.
 
4. Line up the next piece of wallpaper to this plumb line and apply toward the corner as though there were no corner, matching the pattern, and letting the extra paper flop over the corner.
 
5. Using your trim knife again, cut the second strip of paper just a little bit wider than the corner (by 1/16 inch or 1/8 inch), and smooth the paper tight into the corner. (Be careful - as always - not to press too hard with your razor, or you'll damage the wall.)
 
6. Lap the first piece (which you had pulled back a few inches) over the second piece; this will ensure that if the paper shrinks, no gap will appear between the two strips.
 
7. Press down the paper and clean off any adhesive that has squeezed out.
 
8. Apply the same basic strategy to outside corners, perhaps using a straightedge to keep your razor cuts straight.