If your indoor unit is electric and not gas or oil, then your problem is either in the control wiring or a relay. With your circuit breaker OFF: Start by removing the wire on "G" at your control board. If you have an older model, there might be a wire nut connection for your thermostat wires.......disconnect the wire nut with the green wire which is the most commonly colored wire used to control the fan. Tape off the end of the wire to prevent it from shorting......turn the breaker on. If the blower continues to run, you have a problem with a relay. If the unit is heating while the fan is running, you most likely have a stuck heating sequencer. If there is no heat, you most likely have a stuck fan relay.

Here is a video to help you identify heat relays/sequencers and fan relays. Having a stuck fan/blower relay is a fairly common problem. Often, you can gently tap the relay to "free" it and stop the fan. However, once they start "sticking", they will continue to do so.
I hope you find this information to be very helpful to you, moving forward. :-)

My mony is on a fan limit switch....