Yesterday I potted up suckers of Hydrangea longipes and Sarcococca hookeriana ’Lance Leaf’. Suckers are adventitious shoots meaning they grow not where they typically do, going up. They grow out of the crown horizontally under the soil until they pop up some distance away from the plant, which in general makes them a nuisance, particularly with grafted roses as the stronger rootstock will shoot suckers which draw energy from the plant and isn't the rose you wanted.
But they are handy for propagation, as if they are not grafted then they are true to type plants that are minimal effort because they propagate themselves.
I simply get a fork and wiggle the soil free around the sucker until I find a good clump of root preferably close to the base (so I can fit it in a pot), then sever it and pot it up. I was lucky with these H. longipes as they are all quite uniform in growth, though because they grow horizontally and then turn vertical I have to pot them at a weird angle so staking is needed to get them on the right track.
I do this now in spring as they have roots and once severed from mother plant will now put all its own energy into forming a good root system, was able to pot mine into 2 litre pots and be content they will fill it out quite soon, but not all will be like this so play it by ear if you try this out.