Growing roses from seed can be challenging, since the majority of seeds you collect often won't germinate regardless of your efforts. Fortunately, most rose plants produce a large quantity of seeds inside their rose hips, so it usually isn't necessary to achieve a high success rate. Keep in mind that the plants that grow may be different in appearance or other characteristics from the mother plant, especially if that plant is a hybrid of two varieties grafted together.
While your cuttings take root, keep them covered and moist. In a garden bed, a simple DIY mini greenhouse does the trick. Just place a bell jar, a garden cloche or an overturned mason jar over the cutting. A clear plastic bottle with the bottom cut out and the cap removed works, too. Water the soil regularly to keep it moist, but not soggy. Your mini hothouse will keep the humidity high inside.
Cover the cutting loosely, pot and all, with a plastic bag or plastic wrap and keep the soil moist. Putting a tall stake into the pot will hold the plastic away from the leaves. If the plastic touches the leaves, they remain wet and can succumb to a fungus disease. Along the same lines, make sure the condensation can escape from the plastic or the stem will rot.