How to keep it happy
Begonias love bright indirect light and to have soil that is kept consistently moist. You don't want to have soggy soil, or have the roots sitting in standing water, but if the top of the soil feels like it is just beginning to dry out, go ahead and water.
There are many different varieties of begonia, some with more spectacular foliage, like the angel wing types or begonia rex, while some are more popular for their colourful flowers. With any begonia, humidity is a must. Keep your plants away from any drafty areas or heating/cooling vents. A humidifier is a great idea, especially for the dryer months of the year.
While you don't want a draft to affect your plant, you do want good air flow, so keeping a fan in the same room is helpful. Without airflow, plants that like moist soil may end growing mold at the soil level and they will have a hard time drying out.
Misting your begonia is fine, to help increase humidity, but you do want to choose a device that helps you get a very fine mist. Many begonia have fuzzy foliage and do not like to stay too wet.
When your begonia is through flowering, deadhead any blossoms with pruners or simply pinch them off with your fingertips.
This plant is toxic to cats and dogs.
Begonia can grow several feet tall. Try giving them a coir pole or a trellis to use for support.
Troubleshooting your plant
Brown edges, crispy feeling foliage = not enough humidity
Mushy stems, especially near soil = too much water, not enough airflow