Pictured: the final result of propagating a rose from a bouquet.
Start with roses from the store or a florist. Pick a few that look the healthiest and lop off most of the top of the stem, leaving any leaves.
Cut the bottom of each stem at an angle and immediately put each in a separate glass of filtered water. Put those in a sunny window.
Wait two weeks, topping up the water as needed.
If the roses are sprouting more leaves, good, if not, wait a bit longer.
Once the rose stems start sprouting more leaves, plant them gently in pots or directly outside in good, prepared soil. Water generously.
Keep watering them once every three days or so, usually about 1 cup of water per plant is fine.
After about a month and a half slack on the watering a little bit and keep up the watering schedule like with other potted plants.
NOTE 4/29/2020 I propagated two of these. One kicked the bucket and the other is doing well.