the RHS has instructions on how to do it, either from hardwood or semi ripe cuttings, here's the link:

https://www.rhs.org.uk/advice/profile?PID=153

You'll need to scroll down to propagation, towards the end.

Note that a lot of roses are on a different rootstock - this is done usually to make a stronger plant, because the grafted part, the part you want with the flowers on, isn't a strong grower without a good rootstock, but its still worth trying cuttings to see how they do as they grow.

Many root incredibly easily - I stuck a cut stem in a pot of compost one year and it flowered the next.