I Have a Trane Weathertron Heat Pump and the blower fan doesn't turn off even though is set to automatic however when it reaches the set point the compressor turns off but the fan keeps blowing and never stops. I have to manually turn off the AC Unit flipping the swtch to OFF

What could be the problem?

You likely have a blower relay or heat sequencer that is "stuck" in the closed position.

You likely have a blower relay or heat sequencer that is "stuck" in the closed position.
Thanks , I will try to fix it.

Thanks , I will try to fix it.
If you're a DIY, I suggest that if you must do the repair, verify that power is disconnected at the fan coil and then start by replacing the sequencer(s) first.
Be sure that all wiring connections are marked and end up where they are designated to go.

Sometimes the high limit tripping will force the fan on and stays on until you break power to the unit. Check your filters and make sure the are clean.

If you're a DIY, I suggest that if you must do the repair, verify that power is disconnected at the fan coil and then start by replacing the sequencer(s) first.
Be sure that all wiring connections are marked and end up where they are designated to go.

I would like to see if I can do it myself, but how technically savy must I be to figure this out? How do I identify what the sequencer(s) or the blower relay are? Also, where would both be located, in the air handler in the unit outside? Please be detailed, as I am totally unfamiliar w/AC repair. Also, If I was to get this repaired professionally, what should I expect to pay?

Thx.