The main concern when using nonrenewable resources is, well, that they cannot be reused, so they must be used in a responsible way and be conserved as much as possible.
One way you can conserve a nonrenewable resource is by using it less. For example, if you have a wood fireplace, you don't need to keep it constantly burning, so you let it burn out or put water on it. That way, you need to burn no more wood (even though some consider wood a renewable resource).
Another way you can conserve nonrenewable resources is to manage your water. Water is a very abundant source, but freshwater is harder to find. Wasting it by keeping the water running while you, say, brush your teeth, is wasting it.
The final way you can conserve natural resources is by switching from a standard car to a hybrid or electric car. These need little or no fuel to run.