So grandma had the right idea in the first place, and she really did know what she was doing. It has always been fun to start roses from cuttings. Some people get their kicks by going "rose rustling" in the deserted cemeteries of old and forgotten mining towns. Others just take a twig from their favorite rose and stick it into the ground in their backyard. There is nothing complicated nor scientific about taking cuttings of roses and rooting them to "start" a new plant. There are various ways of taking rose cuttings, so let's tell you how.
The ripened rose hip is then placed on a clean cutting board and cut in half to remove the seeds. Place the seeds in a clean container. Add some diluted bleach to kill off any bacteria and fungus spores. You can make the bleach by mixing drinking water with two teaspoons of household bleach. Stir the seeds well before rinsing them and using bottled water to remove all the bleach. To further clean and disinfect the seeds, put them in the container and add some hydrogen peroxide. The seeds can be soaked for up to 24 hours before rinsing them with clean water to clear all the hydrogen peroxide.
To start rose bush from cuttings, once the rose cuttings have been taken and brought to the planting site, take out a single cutting and remove the lower leaves only. Make a small slit with a sharp knife on one or two sides of the lower portion of the cutting, not a deep cut but just enough to penetrate the outer layer of the cutting. Dip the lower portion of the cutting into a rooting hormone powder.
Grandma's Mason Jar: For the beginner this is probably the easiest way to take rose cuttings. Not much equipment is needed, just a clear quart-size glass jar and some cuttings from your favorite rose. For you modern sodapop lovers, a 2-liter plastic bottle with the bottom cut off will work just as well. Cut a piece of rose stem about 6 inches long, remove the bottom set of leaves, and just stick the stem into the ground (or into a pot) a couple inches deep, and cover with a jar or bottle. You will need to periodically water the soil around the jar, otherwise the rose stem will dry out. It will take a couple of months for the rose stem to take root and begin leafing out with its new growth. The best time of year is spring or early fall. If you live in a mild climate, then winter and summer can also be successful for rooting roses. Intense summer heat of 100 degrees is not  conducive for taking rose cuttings, nor are 32 degree or below winters.
America's most popular flower is also one of the very oldest flowers in cultivation. There are over 2,000 different rose varieties to lure us with their history and fragrance. This is because the rose, like the orchid, cross-breeds readily—a trait exploited first by nature, and then by horticulturalists. Today, we can choose from old-fashioned favorites, as well as modern varieties that are the result of intensive breeding programs throughout the world. The rose is a flower with a rich past, and an exciting future.
The rose seeds can be planted right away if you have harvested them as late as November, December or January (in Southern California) or early spring after danger of frosts in your area. Place the rose seeds about one-half inch deep in a very light mixture of 50% sterile potting soil and 50% vermiculite. Some rose hybridizers use Sunshine Mix #4. You can use small pots or shallow trays to plant your seeds, whatever works for the space you have, as long as they have good drainage. Nursery flats work well for this. Lightly dust the rose seeds with RooTone or Captan before covering with soil. And then dust the top of the soil again, which will hopefully help to prevent damp-off (a disease which kills young rose seedlings). Amateur rose hybridizers concerned with toxic chemicals may want to periodically spray the seed tray with diluted peroxide and water instead of the more toxic Captan.   
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.