I'm going to disagree with the above post a little and tell you that you can take cuttings and very successful they can be, but it does depend somewhat on the rose. Old shrub roses, climbers and ramblers are better than modern highly bred hybrid teas as these are better grafted [as above post], but it's worth a try with any of them I think.
The best method is to take 1 foot long cuttings with a heel, in September, supposedly of non flowering shoots but I've used flowering ones too, cut off any side shoots to leave a bare cutting, as I say about a foot long.
Dig a trench about 9 inches deep. Let's say you have 6 1 foot long cuttings to plant. I would put some sharp sand in base of trench and place the cuttings in the trench about 6 inches apart, and fill in with soil leaving about 3 inches of cutting showing above ground. Water in well and forget about them. This trench should be in a shady part of garden, not under trees.
Next Spring they should start showing signs of life. Leave where they are till following autumn by which time you will know if you have a decent plant to grow on or not. If so, dig up and plant in final position in garden.
It's fun to do and worthwhile if you don't mind waiting.