1. The light stuff
East- and west-facing windows (with west being a bit warmer) are perfect for plants like African violets, which do not like to get colder than 65° F. Ivy and asparagus fern prefer the cooler east window. Plants with large leaves to absorb the most light — schefflera, aspidistra, Chinese evergreen, dieffenbachia — will appreciate a bright, unobstructed north window. If that spot is a little too shady, augment the light artificially.
I moved an easy chair near a palm at a north-facing window and placed the floor lamp next to it. When I sit to read a magazine, the plant enjoys some extra light as well.
One more hint: Give plants a quarter turn every so often to keep them growing symmetrically.
2. Soil mastery
I don't use garden soil for potted plants. It's too dense and heavy, and lacks open spaces for oxygen. Potted plants need great drainage, and air for their roots. I don't use prepared mixes, either. They tend to decompose and squeeze out oxygen. Instead I make my own "soil-less" planting medium from humus (my choice is coir — recycled shredded coconut hulls) and perlite (small white chunks of exploded volcanic glass).
Use four parts humus to one part perlite for most plants; more perlite for cacti, less for jungle plants. If you have to buy a bagged medium, look for African violet mix, which tends to have better drainage.
(Note: The terms potting soil and planting medium are used interchangeably.)
The importance of drainage cannot be overstated. An old notion was to fill the bottom quarter of the pot with crocking — broken clay potsherds. But if your medium has good drainage already, the only reason for a piece of crockery, or some pebbles, would be to keep the soil from washing out of or clogging the holes. One concave potsherd over the single hole in a clay pot (or some pebbles for a plastic one) should do the trick.
3. Water works
"Experts" often recommend watering once a week. Wrong. You cannot impose a schedule on a plant, so water plants when they need it. That depends on soil, container type, indoor heat source (forced air is the worst), the weather (whether it's cloudy or sunny), and a host of other factors. Feel the surface of the potting soil. If it feels cool or damp, let the plant alone. If the surface feels dry (or, in a large container, if the top half-inch of medium is dry), water. Soon you will be able to judge this condition by sight. (Inexpensive commercial moisture meters are also helpful.)
Don't fuss over your plants too much. Adding a little bit of water every day leads to root rot — probably the greatest killer of potted plants. Except in a few cases, indoor plants want more water less frequently. Pour the water slowly on the soil until it thoroughly moistens the medium and seeps out the drainage holes. If the saucer beneath the pot fills with water, do your best to empty that. Then wait until the soil feels dry again, which could be in a few days or weeks.
If you see tiny black flies called fungus gnats around your plants, you are overwatering. The insects' larvae eat decaying matter in the soil. To nip gnats, water less often.