When plants grow in rooms with low levels of humidity they will often wither and die. Most plants prefer a humidity of around 60 percent, and anything less will cause water to be pulled from the soil and the leaves of the plant. Providing proper humidity can ensure the health and long life of your plant in much the same way as giving it the correct amount of sunlight. In dire cases, the positive results of upping the level of water vapor in the air (which is what humidity measures) will be seen nearly immediately.
Lower the temperature of your grow room to the coldest temperature tolerable for the plants you're trying to grow. The hotter the room the more likely water will evaporate into the air, drying out the soil.
Set up a humidifier in your grow room. As pointed out by GardenLine, use of a humidifier is one of the most surefire ways to increase humidity.
Line the pot with damp peat moss. You must ensure that the peat moss remains damp at all times, as once it dries out it will become nearly impossible to re-wet. When this happens, you will need to replace the moss.
Group plants with similar watering needs near one another so that if water evaporates from one plant it can be absorbed by another. Keep these plants close to one another, while still allowing them room to grow and branch out.
Hang wet paper towels on a string with clothespins around the grow room as an inexpensive alternative to a humidifier. Replace or re-wet the paper towels when they dry out.
Mist the leaves of the plants with a water bottle. This should not be used as the only method of increasing humidity, as it is one of the least effective methods. It works well when used as a supplementary method only.