The grafting technique usually used for roses is called budding. A small piece of the desirable plant that includes one bud is placed within the bark of another. This rose is called the understock. Once the shoot is several inches long, the top of the understock is cut off just above the new bud. Understock roses are usually easy to propagate. They have a high tolerance for alkaline or acid soil, and can grow in warm temperatures.
In warm climates such as Florida, the species Rosa fortuniana, native to China, is valued as a rootstock for its tolerance to the sandy, nematode-infested soils. This type has white, fragrant, double flowers that are smaller than most hybrids. In northern areas with acid soil, roses are often grafted on to Rosa multiflora, a fast growing shrub with very small, white, single fragrant flowers.
The bud union is somewhat swollen and may have a slightly different texture of bark. It is always below the main branches of the rose. Look for the bud union before you make any cuts. Cut off a dead branch, but only back to the main trunk. Unless branches are dead or diseased, cut them back to no less than a foot above the bud union. A few more feet is OK, but it may depend on your climate and the variety of rose.
Some roses are not grafted because their own root systems are vigorous enough to support them. These roses are easy to propagate from cuttings or seeds. Miniature roses, for instance, are usually grown on their own roots. Many antique or species roses are also grown from cuttings.