Roses may be rooted from cuttings taken in early to mid summer. Mid fall is another good time. Make 4-6" cuttings from new growth that has started to turn woody (not succulent). Remove all but the top two sets of leaves and dip the base of the cutting in a rooting hormone. You can place them in a 50:50 mix of perlite and peat in a rooting chamber or for an easier option stick the cuttings in pre-moistened, rich soil in an area out of direct sunlight, such as the north side of the house under the eaves. Cover the cuttings with an inverted mayonnaise jar. Within a couple of months they should have some roots. Give them another month before carefully digging and replanting. Do more cuttings that you need as not all will be successful.
The following web sites are excellent guides for the details of how to propagate shrubs including roses. They will provide much more detail than we can in this short space:
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