Look at the rose bush and identify the areas where rose buds are dying or beginning to die. You might want to wear gloves while you do this to protect yourself from the rose bush's thorns.
Open the rose pruners so the trimmers are as wide as possible. Slide the pruners down the dying branch to the spot where it meets up with the living part of the bush.
Clip the dying branch off by squeezing the handles of the pruner together. As long as the pruners are sharp, this should be easy. Continue trimming until you have removed every dead rose and branch.
Add the clippings to a compost pile.