I haven't had great luck with cuttings, but one technique that I found works is to wrap the end of the cutting with a ball of sphagnum moss, wrap it tightly with a rubber band, so that the end is definitely in contact with the moss, and plant it in the usual way. I think this works because the moss has antifungal and antibacterial properties, and prevents it from rotting.

I was reading on the Bermuda Rose Society website that spraying with dilute copper sulphate really improves their strike rate too.

That damp parcel technique does look interesting.

I never know whether to remove thorns that will go in the soil. What do you all do with thorns?

Margaret has the runs on the board in successful cuttings department.
My success rate is much patchier. There seems to be quite a bit of alchemy involved.
The method I find easiest is one Patricia taught me.
You need clear plastic party cups, large zip lock bags and a cheap plastic crate with a lid and the potting medium of choice.
Make a few drainage holes in the bottom of the plastic cups..
Fill with potting medium of choice. In the west, Richgro cutting and seed raising mix is good but brickies sand is OK too.
Make sure medium is really well wetted and then well drained. No pockets of dry or water-repellant medium.
Write rose name on outside of cup with a permanent marker.

Select your cutting material. If you have a piece with four eyes, leave the leaves on the top two.
Push cuttings into cup of cutting mix. (One to a cup).
Put cup or cups into large zip-lock bags and seal and then put that into plastic crate. Put plastic crate into that magic spot that isn't too hot or too cold and forget about it for 6 weeks.
After 6 weeks, check. They are generally either black and furry, or have chosen life and you might even be able to see the little white roots against the inside of the clear plastic cup.
When they get to that stage you can open the bag and allow them to gradually acclimatise outside before potting up.

I like this method because you can see when they have grown roots and are ready to pot up into a nourishing potting medium and this can be done with minimal root disturbance.

Also like this advice from 1888 and often take cuttings of Teas, Chinas and Noisettes as suggested here - with that little heel on the end.
"With the exception of the Noisettes and Tea Roses, all grow well and readily from stout cuttings of 4 or 5 eyes, planted in May or June in an open border up to the top-most eye, and kept moist in dry weather. ... The wood of the Noisettes and Tea Roses is very pithy, and on that account it will not callus and root properly. The small spurs from these kinds, however, little twigs, which have borne blooms during the previous season, when taken off the plant with a heel, grow readily, when inserted in a sandy soil and kept damp.
In the first year, they make, of course, only small plants, but being vigorous growers, they soon rapidly increase in size, and the third season will make large specimens of them.
The principal condition in growing Roses from cuttings is to plant early in autumn, before the soil gets too cold."
From The Rosary and the Cultivation of the Rose by “Hortus” in The Western Mail [Perth], February 18, 1888 p11