I bought 1 dozen roses from my local grocery for my wife about 2 weeks ago and these amazing flowers looked good until yesterday.
I was going to throw them out when I noticed some new growth on some of the lower nodes.
I clipped off the stem just above the new growth and left what remained in the Vase.
What do I need to do to ensure that these cuttings root out? I think I have 4 that are showing signs of life but not yet showing roots.

Quite honestly, I think your chances of having good results from this are slim. Most florist roses are very hybridized tea roses and are very seldom, if ever, grown on their own roots. Most hybrid teas are grafted onto a rose with much sturdier root stock. The hybrids aren't developed to be good plants on their own -- they're developed to have long stems and perfect flowers. So you might be better off to just break down and buy a couple of rose bushes -- and if you do, I highly recommend old garden roses that grow on their own roots. You won't get the long-stemmed florist look, but they are beautiful in their own way.

I already have several rose bushes now so I'm not really looking to plant more but If I can get these to root it would be a bonus project.
With that being said what can I do that will give these cuttings the best chance of taking root and surviving?