Rosh Chodesh Elul is two days, and in Elul we say Psalm 27 in both morning and evening. When exactly do we start?
We started saying it tonight.
From here (I added the bolding to the relevant part):
Begin saying L'David Adonai ori v'yish'i (Psalm 27) on the first day (at night) of Elul, not the first day of Rosh Chodesh Elul (the 30th of Av).