When playing as Franklin Clinton, after the mission The Merryweather Heist, he will receive a text from Brother Adrian, asking him to go to their website, to complete the four stages of the C.o.M process.
The player will need to answer a test of multiple choice, it does not matter with answers you choose, the result will always be the same, it will say that Franklin is frustrate with his life and need to find understanding. After this, the player will need to wait some in-game hours to receive a password via e-mail to continue the test. The password will always be FUTILITY, once you receive it, go to the link on the e-mail and write the password to conclude the first stage of the C.o.M process.
To complete the second stage, it will be necessary to donate $199 dollars to the cult. Once you donate it, you will need to resolve a puzzle consisting of forming words with the letters that are presented, once the words are formed a letter is added to a phrase on the bottom of the page. You need to complete the phrase in less than one minute. The first words are: Divine, Completeness, Orthodoxy, Process and Realization.
Its impossible, however, to complete the puzzle in one minute (but according to the order of the first five letters, it most likely that the phrase is "you are an idiot"). Once the time expires, the second stage will be completed.
To continue to the third stage, you will need to donate $4,999 dollars to the cult. The third stage consists of a slide show, that the player need to watch till the end. Click on the link at the bottom of the page in the last slide to complete to continue. Wait a couple of minutes to receive a new e-mail with a new password (ACTUALITY) to write on the website and conclude the third stage.
To continue you will need to do a new donation to the cult, this time of $9,999 dollars. The fourth stage consists of a new test, but now you can only answer "Yes" or "No". Select "Yes" for all questions to complete the last stage and receive your certificate of completion of the C.o.M process.
After this, you will receive a last e-mail from Brother Adrian, confirming that the t-shirt from the C.o.M has been delivered in your wardrobe.
The Cultstoppers website mentions Children of the Mountain as a cult similar to Epsilon and several people in the state of San Andreas also share this confusion in which members reply that Children of the Mountain is not a religion.