Bonsai, "plant in a container", has been practiced for many centuries in Japan, and even longer in China. Most bonsai you purchase will already be established in it's own container.
Mist your bonsai every other day.
Immersing your bonsai in a basin of water was originally thought to be the best way to thoroughly water a bonsai. However, many owners found that they lost their rock and much of their potting medium by doing so. An easier watering method is to use a watering can that allows watering from the top so that you do not wash rock and soil away with each watering. Water slowly, ensuring saturation of the bonsai root system. Water should be seen dripping from the drainage holes in the bottom of the bonsai container.
Depending on the size of the bonsai and it's container, watering will range from daily to once a week. As with any house plant you will eventually learn when your bonsai needs water by feel or by use of a water meter. Bonsai typically will require more water during the summer months.
If you have purchased a bonsai that stays outdoors, watering will depend on how many hours it stays in the sun, and the size of the container. Before first frost, move your bonsai to a protected area, such as under a porch with southern exposure, and protect with some mulch or leaves around the container. In the spring, after danger of frost has passed, the bonsai may be brought out of the protected area.