The stem of my Dracaena is becoming black. What's wrong with it?
Do you have any yellowing on the leaves prior to the stem color issues?
Soil should be moist but never soggy. Root rot may be the issue with your plant.
Always check the soil before watering and make sure the pot is draining away any excess water.
If the Root Rot is extensive, you plant may not recover. If the plant lifts easily from the soil, it has rotted. You will want to discard your plant and perhaps try again.
Also salts can build up in the soil and harm the leaves and the plant. Generally you would see the tips of leaves turning dark or black.
Using distilled water for watering will generally help with this condition.
Here is a link to refresh you on the care requirements.