Aah the 13th of August and on the full moon at that! It was said that Aradia, in the form of a physical woman on earth was born on the 13th of August, the day of Diana in the year 1313 who then roamed the earth teaching Witchcraft, aptly named 'La Bella Pellegrina' or 'The Beautiful Pilgrim.' A great deal more detail on Aradia can be read in my previous post here. You can also read a brief description about Hecate here.
In the northern hemisphere, Hecate is honored by leaving an offering at the crossroad - the roads between life and death which she represents. Take a plate you won't mind 'losing' to the crossroads with goods such as honey (lavendar honey is the best), eggs and garlic out once darkness has fallen - say your invocation to the Goddess of Witchcraft and leave the plate there and do not go back for it - in fact, once you turn around and journey back home, don't look back to that crossroad. In the home, burn patchouli incense, a black candle and performing divination at midnight. Hecate observes all activity & assists at night, so perform all of the above at night time.
Seeing as it's a full moon you may feel inspired upon drawing down the moon to repeat the charge of the goddess in its original form from Aradia: The Gospel of the Witches by Charles Leland below (before it was changed by Doreen Valiente and Aleister Crowley before her) to honor both Aradia and Diana:
When I have departed from this world
Whenever ye have need of anything
Once in the month, and when the moon is full
Ye shall assemble in some desert place,
Or in a forest all together join
To adore the potent spirit of your Queen,
My mother, great Diana. She who fain
Would learn all sorcery yet has not won
Its deepest secrets, them my mother will
Teach her, in truth all things yet unknown.
And ye shall all be freed from slavery,
And so ye shall be free in everything;
And as a sign that ye are truly free,
Ye shall be naked in your rites, both men
And women also: this shall last until
The last of your oppressors shall be dead;
And ye shall make the game of Benevento,
Extinguishing the lights, and after that
Shall hold your supper thus