My (very)rough drafts:
1: Set up the board.
2: Place a Doom Token reversed to show an Elder Sign and an upside down Gate on each Unstable Location to represent a Sealed Gate, along with one Clue Token. A Gate can be unsealed by using 5 Clue Tokens (and possibly some other ways), and you win when all of the Gates are Unsealed and all of the Doom Tokens are placed on the Ancient One's card thereby awakening him.
3: Choose First Player as normal.
4: Choose a random Cultist in the way you would normally pick an Investigator.
5: Choose an Ancient One. This will be the Ancient One you are trying to awaken by unsealing the Gates. When a Gate is unsealed, the Elder Sign on it is flipped over and the Doom Token is placed on the Ancient One's card. You then draw Monsters from the cup until you get two of the appropriate Dimensional Symbol and place them with the Gate. When all of the Gates are unsealed the Ancient One awakens and the Cultists win. In this variant the Ancient Ones look rather like the Guardian Cards in the standard game. They provide a specific bonus of some kind, with possibly an enhanced Bonus for Cultists with the appropriate Dimensional Symbol or for Dark Allies who have the appropriate Ancient Ones name listed in their Ability.
6: Choose an Opponent. These are the good guys trying to stop the Cultists (or possibly a rival Cult or race of monsters). They will use a format similar to the Ancient Ones from the regular game, and instead of Doom Tokens you place Success Tokens on their Track. If the Track fills up, they have caught up to the Cultists who must fight them.
7: Separate Decks as usual.
8: Receive Fixed Possessions as usual.
9: Shuffle Investigator Decks as usual.
10: Receive Random Possessions as usual.
11: Finish Cultist setup, which is pretty much the same as Investigator setup.
12: Create Monster Cup as usual, and place the Townsfolk Sheet. Townsfolk are similar to Monsters from the regular game, but they oppose the Cultists. Instead of drawing them from a cup you roll on the sheet for the encounter (this helps because you have less tokns to print out).
13: Shuffle the Gate, Event, and Location decks. Event Cards are similar to Mythos Cards, and like them are divided into Environments, Headlines, and Rumors. Unlike Mythos Cards they do not open Gates or summon Monsters (unless the Text says otherwise), or move Monsters (unless the Text says otherwise). They may however, generate Townsfolk (see below). You will basically draw an Event, place an appropriate Clue Token, place a Success Token on the Opponents Track, and read the text to see what happens next.
14: Place Cultist Markers.
15: Draw and Resolve Event Card.
Order of Play
Upkeep and Movement are unchanged.
Arkham Encounters are mostly unchanged, but you are only drawn through unsealed gates if you wish to go (Event cards or Location encounters may change this, Gates opening as a result of a Location or Event Card still pull Cultists through unless they have the appropriate Dimensional Symbol.). Unsealing Gates requires a Fight or Lore Check and the expenditure of 5 Clue Tokens, and is done on the Encounter Phase (similar to Sealing a Gate in the normal game).
Otherworld Encounters are mostly unchanged depending on if the Dimensional Symbol of your Cultist Ability matches that of the Gate you went through.
The Mythos Phase is now called the Investigator Phase. You draw an event card, spawn Townsfolk, place clue tokens, and move Townsfolk. You then read the text of the card and follow it as usual.
The Terror Track When there are a number of Monsters on the board equal to the number of Cultists the Terror Level increases by one. Like normal this can cause locations to close, but you do no return Ally cards to the box as the effects of terror are not something the sort of Ally you possess would be vulnerable to. On any turn in which 3 or more Townsfolk who are considered Important are killed or removed from the board the Terror Level increases by 1.
There are 2 Types of Cultists: Cultists and Dark Allies. A Cultist is a worshiper of an Ancient One. A Dark Ally is in league with a specific race of Monsters such as the Ghouls or the Mi-Go.
In the case of Cultists their Ability will read as follows: Cultist: (Dimensional Symbol) When encountering Monsters with that Dimensional Symbol (or a Cultist Token) you do not need to make Horror or Combat Checks against them unless you wish to, as they consider you one of their own. When encountering Open Gates with that Dimensional Symbol you are not drawn through unless you wish to be. If the Ancient One being used has a matching Dimensional Symbol it may grant you additional abilities.
In the case of a Dark Ally their Ability will read as follows: Dark Ally: (One or more Monsters), (Ancient One) When encountering Monsters named in your Ability (or a Cultist Token) you do not need to make Horror or Combat Checks against them unless you wish to, as they consider you one of their own. During the Encounter Phase you may choose to take one of the Monsters as an Ally Card if it shares your Street or Location, removing it from the board. If the Ancient One being used is the One named in your Ability it may grant you additional abilities.