There are so many different furnace filters on the market that there is not one change cycle stand (once a month, every quarter, twice a year, etc.).
However, there are some tell tale signs that you need to change your furnace filter:
1) You notice your furnace is running a long time in order to heat or cool your home (assuming no excessive outside air temp. Really cold or really hot). When you have a dirty air filter it restrics the flow of air through your furnace. The air carries the heat. Less air, less heat (or cooling) .
2) You hear a high pitched noise from your furnace. This is the sound of restricted air flow or a blower motor that is struggling to suck air.
3) A burning smell. This may be your blower motor overheating or your actual furnace filter overheating. Your furnace needs airflow to keep itself from overheating. If it overheats and your safety switches do not work it becomes a very dangerous appliance.
4) If your furnace stops working. Check your air filter. If the filter is plugged up, change it and try to start your furnace.
A plugged furnace filter will costs you in many ways. Your gas costs will be high, your electrical costs will be higher. Your equipment life will be significantly shorter. It pays to change your air filter regularly!