Normally, you would make a cutting from a nice stem joint. Leave a couple of healthy leaves and bury the joint in potting medium. Wait until roots form.
With this method, you will do it differently. Cut and discard the flower and soft tissue from a straight rose stem. Cut the remaining stem into about three inch lengths. Dip the bottom end into rooting hormone. Very gently, place stems in clear water in a clear glass container. With clear glass, you can watch for the roots to appear.
As soon as the roots start to form, place in pots. One year, I left the hospital at the time they should have been transplanted. Since I was too weak to do so, I came up with a better system. Take an aquarium air pump and feed the air into larger glass containers. Place the cuttings in this with a very small amount of plant food. The air dissolves into the water and supplies the plant with all it needs. The roots grow well. The plants can stay in this for several weeks. The roots grow better than in soil.
Some roses will produce new stems and leaves before the roots are fully formed. This is another good reason for being able to see the roots. When you transplant, keep moist (not wet) and out of direct wind or sun for two weeks.
Many gardeners like to root roses in baggies or other enclosed type containers. These systems work, but they invite fungus and other diseases. Also, more work is involved and you can't see the roots.
Now, we come to the important part. You can get thousands of rose stems ready to cut and root for free. Free is good. Every cemetery has visitors who place cut roses on graves. The caretakers throw them out when the flowers die. All those stems are still viable if less than a week old. See the caretaker and get permission to pick them up. You can do the same with hospitals, nursing homes and some wedding chapels. Some florist will give you the flowers that are too old to sell. I worked at a wholesale florist. On Saturday, we would feel the rose buds. Any buds that felt soft were thrown away or given to nursing homes. Soft buds should never be sold.
Many of the stems will have no thorns or leaves. The florist have a gadget that strips the thorns. These stems will root. While rooting, many will form new leaves.
You can root thousands of plants from these free discards. They will sell for thousands of dollars.