The makeover shows don't show all the work it really takes. Here's the steps you will need to do.
1) Check for loose paper and remove anything that is loose. Simply peel off or scrape any wallpaper that is loose. Pay attention to the seams. If they are curled or raised you need to scrape them level with the rest of the wall.
2) Prime with a tinted shellac primer. You must use a tinted shellac, any other primer could cause the wallpaper to bubble.
3) Use drywall mud to smooth out the imperfections and seams. Sand smooth then seal with a primer. The tinted shellac will work or use any good primer.
4) Now you can paint. Use any good paint. I recommend a low sheen. The lower sheen won't show imperfections as a higher sheen will.
You could prime then fix some things, holes, then paint without mudding over the seams, but they will show.