Growing roses from seeds can be a bit tricky and requires a great deal of patience. As rosemom mentioned, the seeds may not produce the same plants as the "mother" since most roses in garden centers are hybrids. Some of the prettiest roses have been "accidents" though.
A number of years ago I found rose seeds in the Thompson and Morgan catalog and decided to give it a try. The catalog cautioned that germination was slow and only a small percentage would germinate.
I filled my containers with a good potting soil, and buried the seeds to the proper depth. I misted the seeds with water, covered them with plastic wrap, and placed them under gro-lights. Misting with an aerosol bottle is key when starting seeds, since you don't want to drown the seeds and too much water in the soil will make them rot. The mister also doesn't disturb the soil.
Keep the plastic on the pots until you start to see green shoots appear. Again, it could take many weeks and even a few months, but just be patient. I had 4 roses germinate and when they were only about 6" high they produced buds. The buds were very tiny, but absolutely perfect examples of pink mini hybrid tea-type roses. I waited a few months and planted them in my garden with my other mini roses.
This is over 10 years ago and they are still growing. The key with any plant that is more difficult to start from seed is to be patient and not give up. Just have fun and enjoy the process, and if it doesn't work the first time keep trying.
By Lilly M from NW MI
