Proper dead heading of roses
Most roses fall into 2 groups:
1. Floribundas and hybrid teas
2. Repeat flowering roses.
To dead head hybrid teas and floribundas you would remove a spent flower and the cane beneath it back to the first outward-facing leaf with leaflets. Dead heading back to a leaf with fewer leaflets often results in non-flowering new growth, cal "blind wood".
To dead head repeat-flowering roses like shrub roses and climbers, this can be more variable. New flowering wood can be produced from a bud at the bract beneath a flower or from buds at any leaf axis. On these roses, it is better to dead head back to the bract beneath the flower and observe whether new flowering wood grows from this point. If flowers are not produced, prune back to the first leaf and start the observation process again.