There are three standard techniques of cuttings, softwood, semi-ripe and hardwood. None of them involves taking cuttings just now, it is about the worst time for it, too late for hardwood, too early for softwood. Here are advice pages for the three techniques.
Cuttings: softwood / RHS Gardening Advice
Cuttings: semi-ripe / RHS Gardening Advice Cuttings: hardwood / RHS Gardening Advice

Really a good idea to find out what is the name of the plant you like the look of, and google suitable propagation techniques for it. Will avoid you wasting your time. What kind of cutting will take most easily depends upon the species. Some are easy, some are easy enough if you know the special trick for that species, some are challenging, some are impossible. If it costs a lot to buy the plant in a nursery, that is a good indication that cuttings aren't easy!