Growing plants indoors can be as simple or as complicated as you want it to be. All plants require the same basic elements: light, water, carbon dioxide and nutrients. All of these can be easily provided in a specifically controlled indoor environment whether it is as simple as a foliage plant in a window or an elaborate winter vegetable collection.
Light is the most important part of growing plants indoors. This is usually the limiting factor as to what you are able to grow. Many plants need very intense lighting to properly produce flowers or fruits. This can be accomplished with natural lighting through windows, but that it isn't always enough. Some plants, such as indoor grown tomatoes, might be fine in a sunny south facing window but in other locations they may need supplemental lighting from specialized grow lights.
Often the air inside of a house is stagnant, warm, dry and dusty. These are not very good conditions for most plants. Plants like to have constant, even temperatures and humidity levels. This can be achieved by providing some type of air circulation, such as a small fan, near where you are growing plants. Air circulation stirs up stagnant spots and eliminates micro climates that might get too warm or too cold. Avoid growing plants near places that receive cold drafts in the winter which could cause leaf dropping or poor flower bud formation.
Many people want to grow vegetables indoors during the winter when it is too cold to grow them outdoors. Specialized equipment is available to do this including grow lights and elaborate hydroponic setups. The advantage of growing indoors is that you are able to precisely control the growing environment and are not at the mercy of the weather or pests that might invade your garden.
Most of the common houseplants found in garden centers and in the grocery store floral section are able to grow in the normal home environment. These plants have been selected for the market because of their ease of care and tolerance of neglect. Knowing the specific requirements of a type of plant greatly aids in growing success. Often these plants can simply be placed near a window, kept watered and very little care is needed beyond that. Before you purchase a plant, read the tag to see what it likes and only select plants you are able to provide the right conditions for.
Advanced growers may choose to set up a hydroponics system in a dedicated area for growing. Hydroponics is growing plants in water containing all the nutrients they need without the use of soil. The type and amount of nutrients you use depends on the specific type of plants that you will be growing. Many of the indoor, hydroponically-grown crops require high intensity discharge type lighting such as metal halide or high pressure sodium lamps to mimic the full sun that you would find in an outdoor garden. This setup can be expensive, but for many the reward of fresh vegetables in the middle of winter makes it worth it.