Early summer pruning is one of the tasks we are working on right now in order to keep plants shaped, remove branches that are askew or damaged, allow sun to flow through to the ground and remove spent flowers.
For example, the Euonymus in the photo weaves through a chainlink fence and looks nice until its stems poke up above the fence like wild hair blowing in a convertible.
Today, I took cuttings of an heritage azalea at a friend's house before it is pruned for the season. So with the dipping hormones prepared, I took cuttings of a gorgeous tree Euphorbia, some trailing purple petunias and a Salvia that I replant from stem cuttings every year.
Softwood stem cuttings, recently grown stem tips, are tender and have to be handled carefully.They are snipped from plants about this time of year - late spring on the calendar but early summer in the yard.
A tip cutting is the tip bud of the stem and enough stem to hold 3 leaf nodes.
Semi-hardwood cuttings are taken between late summer and early winter, from deciduous and evergreen perennials. Hardwood cuttings are made when the plant is dormant in the winter.
As you prune a favorite perennial, you can take cuttings, dip them in rooting hormone and then stick them into a starting mix, usually a combination of peat moss and pearlite.
The cuttings are protected from direct sunlight, misted regularly to keep them moist and given a few weeks to strike roots. In some plants it's easier than others. But as long as you are doing it for fun and to see if you can fill your garden with plants you made, you'll get a kick out of seeing what works.
I've been reading "Propagation Handbook" by Geoff Bryant. It's a book from Australia, published in 1995.
Better Homes and Gardens link has basic tips.
North Carolina State University link has a list of plants and which type of cuttings to use.
Washington State University link has very helpful photos of the steps, as well as a chart of plants and when to take the cuttings.
Get a bottle of rooting hormone, a bag of peat and pearlite and give it a try. It's free fun and you might end up with a new hobby in the bargain. Once you have a success or two, it will be irrestible to keep trying.