First of all, so we all use the same edition, let's take the text and chronology proposed by Roy Glashan.
The first mention of her name comes in Black Colossus, Story #8 of the internal chronology, published May 1933:
"Let Bel wither my arm! I speak truth! By Derketo, Conan, I am a prince of liars, but I do not lie to an old comrade.Calibre Text-Mark 55,2 / 87
Description of her Cult
Xuthal of the Dusk, also known as The Slithering Shadow was published in September of 1933 as the 11th Conan story. Within Chapter 1, this paragraph appears:
"[...] I have been, and am, the only thing for which a man of them will forgo his lotus-dreams for a space."
She laughed wickedly, flashing her audacious eyes meaningly at Conan
"Of course the women are jealous of me," she continued tranquilly. "They are handsome enough in their yellow-skinned way, but they are dreamy and uncertain as the men, and these latter like me not only for my beauty, but for my reality. I am no dream! Though I have dreamed the dreams of the lotus, I am a normal woman, with earthly emotions and desires. With such these moon-eyed yellow women can not compare.Calibre Text-Mark 36,7 / 76
That is why it would be better for you to cut that girl's throat with your saber, before the men of Xuthal waken and catch her. They will put her through paces she never dreamed of! She is too soft to endure what I have thrived on. I am a daughter of Luxur, and before I had known fifteen summers I had been led through the temples of Derketo, the dusky goddess, and had been initiated into the mysteries. Not that my first years in Xuthal were years of unmodified pleasure! The people of Xuthal have forgotten more than the priestesses of Derketo ever dreamed. They live only for sensual joys. Dreaming or waking, their lives are filled with exotic ecstasies, beyond the ken of ordinary men.
"Damned degenerates!" growled Conan.Calibre Text-Mark 37,6 / 76
For answer Thalis leaned herself against him, slipping one white arm about his bronzed shoulders. Her sleek naked flank pressed against his thigh and the perfume of her foamy hair was in his nostrils.
"Why dare the desert?" she whispered urgently. "Stay here! I will teach you the ways of Xuthal. I will protect you. I will love you! You are a real man: I am sick of these moon-calves who sigh and dream and wake, and dream again. I am hungry for the hard, clean passion of a man from the earth. The blaze of your dynamic eyes makes my heart pound in my bosom, and the touch of your iron-thewed arm maddens me.Calibre Text-Mark 40,2 / 76
This is the biggest and most detailed description we get about the Cult of Derketo, most of it through the telling, behavior and look of her priestess: She has a decadent priesthood of women, they enact in exotic ecstasies, beyond the ken of ordinary men, which is probably a euphemism for sensual or sexual practices outside of what is considered the norm in the world of Conan, and she is the great seductress, more powerful than the lure of Black Lotus.
Derketo is just mentioned in Queen of the Black Coast, the 9th Conan story, published May 1934:
'But the gods are real,' she said, pursuing her own line of thought. 'And above all are the gods of the Shemites—Ishtar and Ashtoreth and Derketo and Adonis.Calibre Text-Mark 30,1 / 86
Derketa in Shem
Another Mention of what might be a misspelling or variation of Derketo (it is spelled Derketa) comes in Red Nails, number 21, published Jul 1936:
"If we ate that we wouldn't need the bite of a dragon," he grunted. "That's what the black people of Kush call the Apples of Derketa. Derketa is the Queen of the Dead. Drink a little of that juice, or spill it on your flesh, and you'd be dead before you could tumble to the foot of this crag."Calibre Text-Mark 23,7 / 180
Moving down to the edge of the leaves, he reached the spear up and carefully thrust the blade through one of the Apples of Derketa, drawing aside to avoid the darkly purple drops that dripped from the pierced fruit. Presently he withdrew the blade and showed her the blue steel stained a dull purplish crimson.Calibre Text-Mark 27,8 / 180
"If your ancestors had thought to dip their spears in the poisonous juice of Derketa's Apples," quoth Conan, with his mouth full, "and jab them in the eyes or mouth or somewhere like that, they'd have seen that dragons are no more immortal than any other chunk of beef. The carcass lies at the edge of the trees, just within the forest. If you don't believe me, go and look for yourself."Calibre Text-Mark 90 / 180
After Howard, Derketo was used in Age of Conan, which has strong ties with Conan Adventures in an Age undreamt of (aka Conan RPG) and some to Conan Exiles. All of them base their depiction of Derketo mainly on Xuthal of the Dusk, also known as The Slithering Shadow and tie in Derketa from Red Nails as a Shemite variant cult to the same goddess/demon.
to Valorum for throwing me the Age of Conan fandom-wiki link.