Short answer
The yearly Shraddha is held on the tithi (lunar day) on which your loved one passed away, in the same lunar month each year, usually on the day that tithi is running in the afternoon. Monthly Tarpanam is usually offered on Amavasya (new Moon). If the tithi is unknown, many families use Amavasya, especially the one closing Mahalaya Paksha, the fortnight for ancestors.
How ChiChakra reads this
Shraddha is traditionally performed in the afternoon part of the day, so the tithi present then decides the date, not the one at sunrise. Some Tamil families count by the solar month of death and its tithi instead. ChiChakra's calendar shows tithis and Amavasya for your city so you can apply your family's rule.
Fixing the date
Note the date, time and city of passing, work out the tithi and lunar month for that moment, and write them down for the family so nobody has to rework it each year.
Each year, look for that tithi in the same month in the city where you will perform the rite. Abroad, it can fall a day apart from the date relatives in India keep.
If the date is uncertain or you miss it, Amavasya, Mahalaya Paksha and, in Tamil homes, Thai and Aadi Amavasya are widely used for remembrance. A sincere offering made late is still an offering, and nothing bad follows from it.
Good to know
Your family priest will know the custom for your community, including who performs the rite and what is offered.