Taking cuttings from impatiens, or many other annuals, is easy and can help scratch the gardener's itch during the off-season. The key is the donor plant that you must remember to bring indoors before the frost kills it. Beyond that, the process is fairly cheap and easy.
mature, donor plant
plastic 4 or 6-packs
scissors, box cutter or other sharp knife
Perlite, Vermiculite or sand
Step 1: Taking the Cuttings
Select branches from the donor plant that are 2-3" long. If possible, take the cutting above a leaf so it will grow to eventually form another branch. Use a sharp scissors or blade to remove the branch. Continue to do this until you have enough cuttings or the donor plant has no more good ones. Keep the cuttings from drying out if you can't plant them right away.
Step 2: Pruning the Cuttings
Remove all of the lower leaves, any buds and any blooms. Leave only 2 or 3 leaves at the very tip of the cutting. If a leaf is bigger than a dime, cut off half of it. There are no roots for the first couple of weeks and the new plant can't support much top growth
Step 3: Planting the Cuttings
Fill your 6-packs with your soil-less rooting material. I use Perlite. Sand is OK but may harbor bacteria that might harm your starts. Work the pencil into the Perlite in a cell. Dip the cut end of a cutting into water and then into the rooting powder. Position the powdered end of the cutting next to the pencil, right where it meets the Perlite. As you remove the pencil, insert the cutting into the space where the pencil was. Or you could just position the cutting in the middle of the cell and fill in around it with Perlite. Be gentle. Impatiens are fairly delicate and you can crush or snap the stem.
Water immediately and water every day if needed. I put my cuttings under fluorescent lights. They provide lots of illumination but not too much heat. The cuttings will look like they are about to die for the first week or so. The leaves are working hard to support new root growth.
Step 4: Transplanting the Starts
In 2-3 weeks you will be able to transplant the cuttings to potting soil. Fill the 6-pack cells about 1/3 to 1/2 way with soil. I work in an old jelly roll pan to contain the mess. Don't pull on the cuttings from the cells. Tip the 6-pack and gently shake the cuttings out. They should have good root growth. Gently tap the root ball to remove any loose Perlite. Place the cutting in a cell and fill the cell with soil. When the 6-pack is full, set it in a container of water so it can absorb moisture and settle the soil around the roots.
Step 5: Take Care of Your Plants.
Impatiens will do well under fluorescent lights. If you start taking cuttings early in the Fall you may be able to take cuttings from your cuttings and more cuttings from those, if you stay on a tight propagation schedule. You can have a few dozen plants from the one you brought in at the end of the normal growing season.
If you have a friend with an impatiens of a color you like, ask for a cutting. Moisten it and take it home in a plastic bag. Keep it out of direct sunlight, extreme heat or cold until you can get the cutting planted.
See my Instructable on building your own light box. https://www.instructables.com/id/Plant-starter-light-boxgrow-your-own/