Even if your wallpaper border is prepasted, you'll still want to purchase border paste to ensure your border is sealed good and tight on the wall. Kids love peeling wallpaper, and I'm sure my mother-in-law can attest to that because her grandkids (which includes my son since he was tall enough to reach) did that to her kitchen. Kids--gotta love 'em.
Measure and cut the wallpaper border to the length of your wall, with about 1/2 inch hanging on each end. For really long walls, it helps to have a 2nd person, like hubs here.
Lay the wallpaper border your counter or table. It doesn't have to be as long as the length of your border, but long enough to give you some room to work with, and it should be a washable surface because you will get paste on it. If you're using a bottle like this one with a sponge roller, roll the paste onto the back side of the border, squeezing the bottle as you do so. If you use a different kind, pour the paste into a bowl and brush on. Make sure to get plenty of paste onto the edges of the border.
You'll want to fold over long pieces of wallpaper border to help stretch it out on your counter or tabletop. This is known as "booking." Booking is very beneficial, not just because it gives you more room to work with. It also helps to keep the paste from drying out, and makes it easier to carry long sheets of border from your work table to the wall. Make sure you fold back to back, front to front, like a paper fan.
So the next step is to put the wallpaper border onto your wall. The job can be made easier with the aid of a chair rail, assuming your chair rail is level on your wall. :-) Put the border on the wall, place the palm of your hands against the border, and gently pull down to line it up against the top edge of your chair rail, or if you're using your ceiling as your border, then push up to line the wallpaper border with the edge of the wall/ceiling.
I'm not sure what this little edger is called, but it's one of the most important tools you'll need. It's flat like a pancake with a hard edge. Use this edge to smoothe out air bubbles & wrinkles, and also to scrape your wallpaper border to the edge of the wall or corners.
Finally, stand back and pat yourself on the back for a job well-done!