Investors & landlords

The inherited property has a new value for you because the day you inherited it, the cost basis for you became the fair market value (FMV) on the date of death.  You would start a rental activity for yourself with with the FMV or other value determined on any inheritance documents.

Stop date is the date of death.

Your Tax Return:  For you, based on the inheritance rules, they will all be new assets to you with a FMV as cost on the date of death. You will treat them like there was never any depreciation or use as a rental on a tax return before you.

1. In your tax return you would not enter any date of sale or disposition.  This will move directly from the trust to you and should all be reported on your tax return, not the trust.
2. Enter each asset on your tax return as though you began operating a rental on the day after your father's death.
3. Use the FMV on the date of death as the cost basis with the following day as your first day to rent the property.
4. Be sure to separate out cost of land and building, you will be asked for both.
5. Enter any other assets that you received with the rental property that will be used for the rental property.  Again, using the FMV on the date of death as your cost basis.
6. Your depreciation will take the appropriate amounts based on the date placed in service on your return. 

Father's Tax Return: (Sending my sympathies)

1. Select the property was disposed of.
2. For each asset use the date of death as the date removed from service.
3. Use the same date as the sales date if necessary and then be sure to select special handling.  Once this is done the only thing on your father's return should be any rental income or expense through the date of death including partial depreciation.  There will be no sale or other documents included with the return.  They are simply removed from service and that is the final return for your father.

Trust Return:

1. The property is transferred to you basically immediately.  It's just passing through the estate to the beneficiary.  Any activity for the rental property should go directly to you and reported by you.  The trust return may have interest or some other income and expense, all of which will likely be distributed to your on a K-1. 
2. Based on your comments you inherited the rental property and all my answers are directed that way. It's unclear if your mother is still part of this process - 'The property was in a trust with just myself and both my parents'.  If she was part owner there could be more complications in regards to the answers above.
   1. Is she still living?
   2. Is she part owner?
   3. Did you receiver her portion as a gift?

@Tax113