This is the technique I use for rooting cuttings in warm weather, based on one developed by Mike Shoup in the US. Used from about late spring to mid-late summer; it needs 6 weeks of warm weather. In autumn, in-ground cuttings give better results.

Cut the bottom corners (about 1 - 2cm) from a zip-lock (food storage) bag - about 32 x 25cm. Bags with a double zip are more reliable.
Put about 10cm depth of a commercial potting mix into the bag An aerator, e.g. handful of Perlite, is recommended in the US, but is probably not necessary if you use a potting mix with good water-holding capacity.
Water it until the mixture is wet through, then close the bag and leave it to drain for several hours.

The cuttings should be taken from a stem that has flowered, up to a pencil-size diameter. For climbers, the cutting should be from a climbing shoot. Some people like to stand their cuttings in water with dilute Seasol (seaweed solution) or willow water for a few days.
Cut off the top bud. Take the leaves off the bottom 2 or 3 nodes (which will go into the potting mix), and leave a few leaves on 2 or 3 upper nodes. (Leafless pieces are much slower, and less likely to succeed.) Re-cut the stem obliquely a little below the lowest node, and dip it immediately into a rooting hormone (some people use honey or water that has had willow stems in it). Make a hole in the potting mix almost to the bottom of the bag, and put the cutting into the hole. A bag will take 3-4 cuttings. Close the bag, and write the name and date on the outside of the bag with a garden marker pen, where they are easily seen. It is not a good idea to put cuttings of different roses into the same bag; it’s too easy to mix them up. (I use Artline garden marker pens, from a stationery shop).

The bags should be put where they will receive light but not direct sunlight. They can be put in groups standing in a cat-litter tray, so they will support each other and are less likely to be knocked over. ( 3-5 per tray, depending on size.) It’s essential that the drainage holes aren’t blocked. It’s important not to disturb the developing roots, but the bag can be opened from time to time to remove fallen leaves or flower buds or dead cuttings (make sure it is sealed properly again afterwards). (You can blow into the bag to plump it up.)

If you can’t see many droplets of moisture on the inside of the bag after a while, add a teaspoon or two of water (or diluted Seasol), but this is rarely necessary.

When good roots are visible in the bottom of the bag (and not before), leave the bag unsealed for a few days to help the plants acclimatise (they may need some water). Then it can be potted out, a few hours after adding water to the bag; scooping out a handful of soil around the roots. (Loss rate from potting out is about 1 in 12; – higher if you take them out before the roots are fairly well-developed.) Tiny pink new leaves usually wilt straight away, and may be better removed. The plant will be top-heavy, and will need shelter from wind for some weeks. Introduce it gradually to sunlight over a couple of weeks. Feed weekly with dilute Seasol alternating with a dilute fertiliser containing trace elements until it is planted out or potted on. Mulching of pots or in-ground plants is important.

As a rough guide: for rambler roses, you can start looking for roots at 3- 4 weeks; for Tea or China roses from about 6 weeks. Hybrid Teas, especially the yellows, are much slower and have a lower success rate.

For cuttings taken in mid-late autumn, in-ground cuttings work best, especially in areas which get some winter frosts, although potted cuttings are another option. Longer cuttings than in ziplock bags are preferable, with at least 2 nodes in the ground, and most of the leaves removed. The larger the piece, the more stored carbohydrate it will have (up to pencil-thickness). They will need mulching, and twice-weekly watering through the summer. It’s best not to dig them up until the winter of the following year.

Looking after baby roses. We suggest watering weekly through the first summer, for in-ground plants. Potted roses may need watering daily, depending on your climate. It's better to remove almost all the flower buds in the first year, so the plant will put its energy into making roots and leaves.