When we bought this house, I had 3 large bathrooms and a kitchen and dining room to de-wallpaper. Ugh - never again. And if you have consider buying a house where they've painted over the wallpaper - RUN!
I used hot water and a mixture of hot water and fabric softener. The real trick was to really saturate the wallpaper with hot water using a sponge, give it a minute or two, spray with a mixture of water and fabric softener and then use a wide scraper to get underneath and then pull slowly. Pulling from the bottom to the top seemed to work best, sometimes - but you'll figure it out once you get the hang of it. You should be able to pull off most of what you adequately got wet. Don't bother scoring the wallpaper with one of those tools - you can wind up making marks on the walls and the scoring sometimes means you have to pull off much smaller bits at one time. Again, the real key is to wet the wallpaper and remove it while it's still wet - so work in manageable areas at a time.
Piranha Wallpaper Remover ( think I got it at Lowe's) also worked well - better than DIF. I preferred fabric softener because it was cheaper, smelled better, kept my hands nice and soft and didnt have all of the "may cause cancer in California" warnings the commercial removers had on them.
Whether you use the fabric softener or a commercial wallpaper remover solution, you'll find you need to rinse your walls well before you paint - even if you're using a primer.
I'll tell you what did NOT work. Renting a (insert about 4 unprintable swear words here) wallpaper steamer from Lowes or HD. What a waste of time and money. It was hot, drippy and totally ineffective. I used it for less than half a wall and then I dragged it out onto the deck and it sat and watched me do the kitchen without it. POS.
Have fun - what a nightmare wallpaper is!