Water Propagation
Water propagation is one of the easiest ways to make more plants. It's a very simple process that allows you to get a cutting to root and give it a better chance at surviving. While it's possible to take your cutting and plant it directly into soil, I've found the most success by letting it root in water and then transplanting when it's ready. The section below describes some of the steps needed for rooting a cutting.
Where to cut
Nodes:
A lot of vining plants like the Golden Pothos or Monstera have raised bumps called nodes that you can see along the stem. Always cut below the node as this is a growth point and where the roots will grow from.
Leaf Cuttings:
Some plants like Tradescantia Zebrina don't have nodes. Cut anywhere along the stem to propagate.
The Red Prayer plant also doesn't have nodes. You can cut at a Y junction in these plants.
Offsets:
Some plants like the Pilea plant produce offsets or "pups" that can be separated from the mother plant. You can separate and plant directly in the soil or water propagate.
You can water propagate succulents, tomatoes, and a variety of houseplants with great success following these guidelines.
Water
Place your cuttings into room temp water. Many plants can handle tap water without issue, but certain plants like the Red Prayer plant or carnivorous plants are sensitive to chlorine and fluroide in tap water and require distilled or rainwater.
Maintain
Change the water every 1-2 weeks with fresh water. Plants need oxygen to thrive so replacing stagnant water replenishes oxygen and prevents algae from forming. Algae competes with your plant for available oxygen and over time will weaken and kill the plant.