Cultists would be taught by other cultists, of course. Other than that - I see Aklo as having a strong performative aspect, (it is an action as much as a language); hence why just reading a  spell can inadvertently trigger it. I also see it as something like a virus; the problem tends to be getting rid of it, not catching it. 

So, say a PC has to read a spell from the dread English-Aklo Thesaurinomicon that they found chained to the altar to dispel (monster of the week), there would be a significant chance that one or more Aklo terms would implant themselves in that PC's brain, along with some knowledge of how they can be recombined to produce other spells. In other words, as the PC learns spells (eg from books) the GM should give them instruction in how the grammar works; the knowledge of how to use it is built into the language, like a self-executing computer virus.

There is a classic case of this in Charles Dexter Ward:
"Ground as the later text was into his consciousness, the discrepancy disturbed him; and he found himself chanting the first of the formulae aloud in an effort to square the sound he conceived with the letters he found carved."

because naturally you just happen to go around chanting eldritch formulae that you are aware do horrible things.

Worked example:
Special Agent Randolph Carter (Int 15, POW 16) is on the trail of the Loathsome Slime Killer of Bad Ass, Texas. He captures a Thesaurinomicon from the Cult of The Lone Sadoqua, reads and finds that he can dispel the Slime with a spell (GM knowledge: Bind formless Spawn of Tsathoggua) within. (As a PC aid, the text should be clear, as are the letters of Joseph Curwen, that correct pronunciation is vital). He studies it carefully.

The spell Ai! (invocation) Ogthrod (binding) G'yhll-G'nai (squamous, formless thing) N'kai (of the Underworld) Zhro (begone)! costs him 5 POW to learn. Each sacrifice for a word lets him test his POW for an increase and he gets lucky with a 2 point increase.

Randolph now has POW 13 and a Speak Aklo skill of 15 (Int) + 15 (his POW after learning the first word) + 5*5 (5% per word) for a total of 55%. He rolls this to cast the spell successfully when he confronts the Loathsome Slime (a formless spawn of Tsathoggua). Casting a Bind spell also lets him test his POW for an increase if he successfully does POW vs POW for the spell.

Casting the spell successfully costs him 5 MPs and 1d5 SAN. Not that although the casting cost may be lower than vanilla CoC, the sorcerer pays a high price in POW (with the resulting losses of Luck, SAN and
MPs) to learn the spell initially.

Randolph knows 5 words of Aklo, and his brain could handle 8 more (13-5) before leaking out his ears (if he doesn't lose more POW, which he would). He reads on and learns Kadath (the unknown land in the cold waste, that which is forbidden by the gods of earth, the nightmare beyond Koth) at a cost of 1 POW. He can now cast Bind Shoggoth by substituting Kadath for N'Kai in the above spell. He now has a POW of 12, a 6 word Grimoire, and Speak Aklo at 60%. His brain can handle 6 more words. Creative players will probably think of various permutations and combinations of their existing vocabulary.

Randolph is becoming addicted to this sorcerous power. He reads on and discovers that by learning the mysteries of Tsathoggua, he can increase his command of Aklo at a much lower cost.

He pays 1 POW and learns the hypersemantic word/entity Tsathoggua. Tsathoggua is a cognitive chunk incorporating N'Kai, G'yhll-G'nai and Kr'tcho-ya, the sorcerous knowledge which compels (teutonisiced as Karotechia). He tests his POW, but no luck. Randolph's POW is now 11 and his Speak Aklo is 65% but his Grimoire now consists of Tsathoggua, Ai!, Ogthrod, Kadath and Zhro; only 5 words, leaving 6 POW free to learn more. He can substitute Tsathoggua any time he would previously have used N'Kai, G'yhll-G'nai and Kr'tcho-ya or any combination of the three: so casting Bind Formless Spawn would now only cost him 4 MP and 1d4 SAN. Other combinations occur to him: Ai! Tsathoggua Zhro! with Tsathoggua substituting for Kr'tcho-ya is a rather handy 3 MP dispel magic for example.

You can see how, since POW on average decreases as knowledge increases, learning the names of the Great Old Ones becomes more and more tempting. Some people will also luck out with their POW test rolls and become great and powerful sorcerers. The majority will burn their POW quickly and become the shuffling cultists and fawning lackies of the Great and Powerful, with too few MPs left to effectively use the Aklo they know. The innocent/ignorant will tend to have higher POW and hence much more Luck than the average cultists but less than the great sorcerers, which is why it's always easy for Indiana Jones to escape the fiendish cult deathtrap, but not to confront the Evil Mastermind. Just to stroke my ego for a moment, this "built in cult" dynamic to the system is something I am rather pleased with.

When Randolph casts his new Dispel spell using Tsathoggua, he attracts the attention (Contact) of the sleepy toad god. Tsathoggua sends him dreams and visions of sorcerous power, and he becomes more and more tempted to reform the Cult of the Lone Sadoqua with himself as the leader...