There are several types of roses, such as ever-bloomers and recurrent bloomers, which require different pruning techniques. There are a few good rules of thumb, however, which you can use on any rose, only it may not encourage the most flowers.
To encourage more flowers, use a dead-heading technique. When a flower is spent, follow the stem down to the first leaflet which has five leaves on it. The leaflets closest to the flower will only have two or three leaves. Select a five-leaved leaflet which is facing the outside of the plant, not toward the interior. Cut the stem just above that leaflet, on an angle. That is where the next stem will emerge.
To encourage the overall health of the plant, remove any stems which are dead, diseased, crossing or skimpy. Remove those as close to the parent stem as possible. Also remove any “suckers”, which are stems emerging from the roots of the plant rather than from the crown.
Fall pruning techniques depend on the variety of rose you have, and where you live. In the spring, remove any stems which have been winter-killed, cutting them back to the parent stem, or to a strong, outward-facing bud