You can do a simple analysis to give you an idea of what might be wrong. After the car has been running for a while, feel the top radiator hose. It should be nice and hot. Also feel the hoses that run to and from the heater core.
If the heater hoses are both hot, that means that hot coolant is circulating through the core and the problem is not the thermostat, or the heater core, but in the air flap or door that directs air to pass through the heater core and into the cabin.
If the radiator hose is hot but both heater hoses are cold, you've got no coolant flow through the heater core. This could be caused by low coolant or an air bubble that is blocking flow, or a plugged heater core.
If one heater hose is hot and the other is cold and you are not getting any heat out of the ducts, then there is a restriction of flow.
If your thermostat is stuck open or not letting the coolant heat up, you should notice that the top hose to the radiator never gets really hot. Check the hoses on a car with a heater that is working well and you will see what I mean.
Be careful where you put your hands when the engine is running, and don't let your clothing or hair dangle around moving belts!