In H. P. Lovecraft's "The Shadow over Innsmouth", there are two instances where a Shoggoth is mentioned. Once by Zadok Allen, when hinting at the plans of the Innsmouth people, and once towards the end, when the narrator sees one in a dream:
“Yew want to know what the reel horror is, hey? Wal, it’s this—it ain’t what them fish devils hez done, but what they’re a-goin’ to do! They’re a-bringin’ things up aout o’ whar they come from into the taown—ben doin’ it fer years, an’ slackenin’ up lately. Them haouses north o’ the river betwixt Water an’ Main Streets is full of ’em—them devils an’ what they brung—an’ when they git ready. . . . I say, when they git ready . . . ever hear tell of a shoggoth? . . .
“Hey, d’ye hear me? I tell ye I know what them things be—I seen ’em one night when . . . EH—AHHHH—AH! E’YAAHHHH. . . .”
"The Shadow over Innsmouth", chapter 3
I met also that which had been her grandmother. For eighty thousand years Pth’thya-l’yi had lived in Y’ha-nthlei, and thither she had gone back after Obed Marsh was dead. Y’ha-nthlei was not destroyed when the upper-earth men shot death into the sea. It was hurt, but not destroyed. The Deep Ones could never be destroyed, even though the palaeogean magic of the forgotten Old Ones might sometimes check them. For the present they would rest; but some day, if they remembered, they would rise again for the tribute Great Cthulhu craved. It would be a city greater than Innsmouth next time. They had planned to spread, and had brought up that which would help them, but now they must wait once more. For bringing the upper-earth men’s death I must do a penance, but that would not be heavy. This was the dream in which I saw a shoggoth for the first time, and the sight set me awake in a frenzy of screaming. That morning the mirror definitely told me I had acquired the Innsmouth look.
"The Shadow over Innsmouth", chapter 5
However, in "At the Mountains of Madness", we learn that Shoggoths were created by the Elder Things (Old Ones), not the Deep Ones, and that the Elder Things were in conflict with the Deep Ones and Cthulhu-kind.
Another race—a land race of beings shaped like octopi and probably corresponding to the fabulous pre-human spawn of Cthulhu—soon began filtering down from cosmic infinity and precipitated a monstrous war which for a time drove the Old Ones wholly back to the sea—a colossal blow in view of the increasing land settlements. Later peace was made, and the new lands were given to the Cthulhu spawn whilst the Old Ones held the sea and the older lands.
"At the Mountains of Madness", chapter 7
Of course, the Shoggoths then achieved intelligence, overthrew their Old One masters, and essentially wiped them out, taking over the Antarctic for themselves.
What I'm missing is the connection between the Deep Ones of Y'ha-nlthei and the Shoggoths. Was some alliance between the two formed? Did the Deep Ones manage to enslave the Shoggoths that the Old Ones of the sea had used? How would the Deep Ones be using a Shoggoth, and what do they plan to do with it?