If your heating system turns on when it should, but isn't blowing out warm air properly, then you may be looking at one of the following issues:
Dirty air filter.
When your heat pump's air filter is clogged with dirt and debris, it obstructs the air flow to the compressor, the component that actually heats the air. Fortunately, this problem comes with a quick and simple solution: replace your dirty air filter with a clean one.
Unit blockage.
Heat pumps are designed to pull heat from the air outside your home. If your unit's air flow is obstructed by fallen snow, ice, a pile of leaves, or any other type of debris, then it will be very difficult for your system to function properly. Again, the solution to this issue is simple: clear away the debris that blocks your unit from receiving an adequate air supply.
Low refrigerant charge.
In a heat pump, the refrigerant is what allows your system to perform heat exchange operations. In winter, the refrigerant absorbs heat from your unit's outdoor coils and transfers that heat to the indoor coils, thus enabling the circulation of warm air. If your refrigerant levels are low (typically from a leak) then your system will blow air throughout the home, but it won't be as warm as it should be. You'll need to call in a professional to check your levels and recharge your system as needed.
Flame sensor issues.
The flame sensor in a gas furnace ensures that a flow of gas exists only when a flame is there to properly ignite it. If your flame sensor is dirty or damaged, then it will cause your furnace to function improperly. Only inspect and clean your flame sensor if you feel comfortable doing so, otherwise, call in a qualified HVAC tech for help.
Air in the lines.
If you have an oil furnace that is not heating as it should and also hear knocking sounds, then you may have air in the supply lines. Bleeding the lines is not extremely difficult, but does require a certain level of knowledge. If you're not confident in your ability to successfully purge the air from the system, contact a professional.