The soil in your potted plant is moldy principally because it’s too wet. In other words, you’re not letting the soil get dry enough before you add more water. Testing soil moisture with a moisture meter or a simple wooden dowel may help you change your watering habits. Here’s more in-depth info on watering plants - Marlie Graves's answer to How often should I water my houseplants?

I’m going to go on a bit with my understanding of certain things that have been brought up by other answers -

• Dumping out moldy soil and rinsing all the roots - very common advice in houseplant books etc. However, I’ve found something else (30 years, 10’s of 1000’s of plants): if you just let the soil dry naturally, the anaerobic microbes that cause root rot are stopped, the dead roots become part of the organics of the soil, new roots begin to grow, you avoid all the stress on the plant of tearing off so many of its vital root hairs, which stresses an already stressed plant even farther.
• Soil is moldy because it’s too wet. Some mold might grow on organic bits, but mostly that’s not the issue. Most packaged potting soil has several sizes of organic particles in it - they may be called “bark fines,” “forest products,” or “compost.” Also, coffee or tea don’t support mold unless they contain sugar and dairy products - those should never be poured into plants.
• It’s true that moldy soil is suffering from reduced air flow - but that’s caused mainly by there being too much moisture in the soil. Air flow isn’t increased by putting rocks in the bottom of the pot, it’s increased by using soil that has good drainage (properly sized particles, a good mix of sand, silt and clay) and by letting the soil aerate (letting the water leave the soil) between waterings. Putting rocks in the bottom of the pot for “drainage” is kind of an old-time plant care myth. It’s easily proven that holes in the bottom of the pot allow most of the water to drain out - no need for rocks. At the same time, a certain percentage of moisture stays in the soil above the drainage area, so, if you have a bunch of rocks there, the moisture still collects above the rocks. All the rocks do is reduce the amount of soil for roots to grow in. It’s called the perched water table, if you’d like more about it.

Should You Put Gravel or Rocks at the Bottom of Plant Pots for Drainage?