Rose bushes are fruit trees in disguise and they will attempt to "set fruit." When you remove the spent blossoms, you interrupt the fruiting cycle and stimulate the plant to fruit again, producing another bloom cycle. If you don't cut the blossoms, they become the "hip" or seed pod and the bush stops blooming.
You want to deadhead weekly if not more often. The rule-of-thumb is to cut back the stem to just above an outward-facing bud above a five- or seven-leaflet leaf close to the end of the stem.
The rule-of-thumb assumes the plant is healthy and strong. If not, cut back less. If you own a type of shrub rose, like Rugosa, where hips are part of the display, just clear away the spent petals. After about October 1, do not cut the blossoms to allow the plant to begin to harden for winter.
If you climate is mild, prune roses in the fall, during November. If your area gets frosty, then prune your roses in the spring, around March or April, when it's a bit warmer. Use the following guidelines:
These pruning guidelines can be used for yearly pruning of dormant, planted rose bushes. These are guidelines and things to look for as you prepare to prune your roses. For a detailed picture of the Anatomy of a Rose, click here
For more information specific to your locale, contact your local American Rose Society.