Allow rose hips to develop by leaving dead flowers on the plant. The flowers are typically pollinated by insects, or pollinate themselves in some varieties, so there is no need to pollinate by hand unless you are breeding specific plants together. Leave the flowers on the rose plant without cutting them. After they wither, small fruits known as rose hips will develop in their place.
There will be disappointments along the way, when many rose seeds fail to germinate, or perhaps they do germinate, only to die several weeks later from damp-off disease. Sometimes a rose seedling will turn out to be as ugly as sin, or very sickly, and you will reluctantly have to throw it away. Other times they will be just ho-hum, or look too much like its parent, and therefore have no value. But, just when you don't expect it, you might discover that one of your rose seedlings turns out to be very special.