Thanks! Just what I needed to know.

I use a garden sprayer to really soak the paper. I tape plastic to the baseboards and have two dropcloths underneath...my dropcloths usually get soaked, so I can't imagine not using them. I guess if you were applying the stripping solution out of a bucket with a sponge or with a little squirt bottle then there wouldn't be much excess running onto the floor. But, in order to really soak the paper you need a garden sprayer IMO...without that you are not getting real saturation and the job will just take longer.

I'm sure your wallpaper being removed could be different, but I generally am able to tear away the decorative surface by beginning at a bottom seam corner and gently pulling upward. Then, I dampen the remaining backing paper/glue with warm water using a sponge. Place rolled towels at the baseboard to catch any water run-off. After is has soaked maybe 15 minutes (and a second water application during that time) the paper peels with a stiff and wide putty knife. Mess is minimal. Sometimes I then use Dif to remove any remaining glue residue.

I use a garden sprayer to really soak the paper.

I totaly agree.But I use real masking tape,not the blue kind and rarely have any leaking.If there is, a quick wipe up with a towel will take care of it. I only use Safe and Simple remover which will not harm hardwood flooring.

Thanks everyone for continuing to provide hints here. I'm still learning what works for me, going slowly and trying different things. :-)

I am able to tear away the top decorative surface, as fnmroberts says, so I did that first for a small section, and then taped the plastic as christophern said. For soaking, I had been using a small sprayer and sponge method first, then tried a little Dif (gel) to see if that was easier than the hot water/fabric softener solution. (And I happened to have some of that Dif on hand).

No clear winner: the Dif doesn't drip as fast as the water does, but I seem to use too much Dif to get the same peelability--and the water mixture is cheaper. :-)

My dad suggested to "paint" the Dif on instead of simply spraying it on, and I might try that as an experiment.

I don't mind going slowly and experimenting, as I'm learning as I go. I'm going to have to do more of the house down the road, so might as well practice until I know what works for me. My dad thinks I should rent a steamer and get it done asap, but I think then the floors really would get wet!

Thanks again for the tips on protecting the floor!