Growing plants in water is called Hydroponic cultivation. There are several ways to do this and there are even full systems to grow common indoor plants, herbs, vegetables etc. in water. The most common hydroponic way to grow you plants at home is by using the Passive hydroponic method.
Before placing your plant in water there are some things to consider:
Make sure that your plant can grow in water. Some examples are Devil's ivy, Rubber plant, Jade plant, Spider plant, Peace lily, Monstera etc.
Make sure that the roots are clean from soil and that the container / vase you want to grow it in is clean.
If you use a transparent container: make sure that it doesn't get exposed to direct sunlight since that can focus the sun rays and concentrate them into potentially start a fire.
Plants grown in water of course love water - especially clean water - so whether you keep your pretty plant in a bottle, container, bowl, or in a vase, you’ll need to change the water and clean the vessel from time to time.
HOW TO TAKE CARE OF YOUR HYDROPONIC PLANT
Carefully lift up your plant and place it in a safe spot for now
Pour out all the water
Clean the bottle / bowl / vase / container
If you have pebbles / rocks in the bottom of the vessel, clean them as well
Fill your vessel with clean water
If you like you might also clean the roots of your plant by rinsing it under a soft jet of water
Put your plant back in the vessel
You can also add a few drops of fertilizer (suited for hydroponic cultivation).