Deadheading varies by rose type, but the absolute easiest way is simply to snip off the spent rose at the end of its short stem, above any foliage.
This instantly makes your rose bush look better. Removing spent blooms stops the plant from putting its energies into developing seeds. This spurs the plant to produce more flowers because it thinks it needs to produce seeds.
Hybrid teas need slightly different advice.
The general rule for deadheading hybrid teas is to find the top set of five leaflets, then cut the stem below that, at the second set of five leaflets. However, you won't hurt the rose if you cut it back higher or lower than that.
In late summer to early fall, you can also just cut off the bloom itself. This promotes more foliage and plant growth, which is important for a rose that is heading into a dormant winter period. However, if you do this earlier in the season, the rose produces more flowers on shorter stems. Hybrid teas are prized as long-stem roses, so this practice could defeat that goal.
Prune anywhere below the entire cluster of spent roses where your rose cane (the main stems) are big enough.
Many of today's shrub roses, such as the famous Knock Out, are bred to shed spent blooms, often called self-cleaning, so the good news is that you may never actually need to deadhead them. However, you may want to clean them up based on the way they look. Because shrubs produce flowers only from new growth, deadhead only the flower and its short stem. If you cut off leafy growth, you won't hurt the plant, you'll just lengthen the time it takes to regrow and rebloom.
Many roses need little pruning. However, in spring you should examine your rose to remove dried or dead canes as close to the ground as possible.
Spring is also the best time to cut back the tops of rose bushes to a uniform shape.
Avoid pruning in the fall. Because pruning of any type spurs more growth, stop deadheading or cutting blooms for bouquets a few weeks before your first frost. As the weather gets colder, roses begin to go dormant, moving their food reserves into their roots. If you prune, this process stops.
You may, however, prune tall modern roses such as hybrid teas and grandifloras down to about 4 feet tall in the fall. This pruning, called "heading back," helps keep them from whipping in the winter winds.