Darlene, it depends on the paper. Many vinyl and vinyl-face papers are "strippable." Simply start at a corner, and begin pulling. You will remove the face, and leave the thin paper backing. You now have 2 options:
1. If the paper backing was left pretty consistently on the wall (meaning it was adhered well), you can touch up any uneven areas with drywall compound, lightly sand, then use a good wallpaper sizing.
2. Once the surface has been removed, spray the wall with a mixture of 2 cups white vinegar to 1 gallon warm water in a pump-up garden sprayer, wait 5 minutes and spray again, then use a putty knife to remove the paper backing. Finish by wiping the wall with a sponge dampened in the same mix.
If your paper is not a strippable paper, you'll know right away, because you won't be able to pull off large amounts at one time. In this instance, use method #2, but you'll need to wet it more times to soak through to the glue. When it's ready, the paper will come off without a lot of work. Testing your times and wetness will tell you what it takes to remove yours the easiest.
Now for the big question, Darlene; is your new trim smaller, so it won't cover? Or altered in areas? If not, it is usually possible to replace trim without repapering.