The Yellow Sign is a...different faction, and not just because they have two Great Old Ones and a few "do this, then do something else" spellbooks.
When we started learning and playing the game I handled it just like I did the Black Goat: I sent out a pair of Cultists to build some Gates in adjacent zones, and then on the second round I Awakened my Great Old One and started Summoning monsters to defend myself.
This was a huge mistake that cost me the game, as by the time I amassed a horde of Undead and started moving about trying to Desecrate zones in order to get spellbooks, Melissa had already build up a formidable force of Shoggoths and Star Spawn.
This, along with Cthulhu's Submerge spell, allowed her to drop in on my starting zone and utterly decimate everything. I think at the time I was rolling a grand total of 4-5 dice, since the King in Yellow has no Combat and you need pretty much all of your Undead out to make them worth anything.
The second time, rather than just wing it and learn as I played, I took the time to read the faction sheet and spellbooks. Once I saw how the abilities and units worked and interacted, I developed a new strategy that differed greatly from what I was use to, and in the end I was much more successful.
So, to help others avoid making the same mistakes, here're my thoughts and strategies for the Yellow Sign. Note this is only applicable to the Core Game: we haven't used any other expansions, yet.
There's nothing special about these guys (unlike, say, Black Goat cultists with the Frenzy spellbook), but if you have the Passion spellbook you gain 1 Power whenever you lose one.
It's basically paying you back for the cost of having to Recruit another Cultist later (though you could get one back for free with a Desecrate attempt), but it's still better than nothing.
These are your heavy hitters, which honestly isn't saying much. Their Combat is one higher than the number of Byakhee in a zone, meaning that worst case they're on par with most other monsters, and best case still puts them behind, say, a trio of Dark Young (though they could still soak up one more Kill/Pain result).
Another nice thing about them, besides getting them for free with a Desecrate attempt, is that with the spellbook Shriek of the Byakhee you can move any of them to a zone of your choice for just 1 Power.
The only other monster you can Summon, but you probably won't bother since you can get them via Desecrate attempts. In contrast to the Byakhee their Combat is one less than the total number of Undead in a zone. This means that if there's only one, you don't get to roll any dice at all, and even with six you're still just rolling 5.
The upside is that it's easy to get them for free, they're always useful for absorbing Kill and Pain results, and you need them for Zingaya.
The King in Yellow
The first Great Old One you can Awaken. He has no Combat, but he's required to Awaken Hastur and can Desecrate zones. Desecrate nets you a free monster or Cultist whether you succeed or fail, has the potential to garner you extra Power, and is necessary for three of your spellbooks (of which you need all six to win).
You can summon him in any area without a gate, which works out great because unlike other factions you don't really want to waste time building them yourself anyway (or, at least not too many). At a paltry cost of 4 Power he's also Cthulhu's Second Coming cheap.
Your other Great Old One has a Combat equal to the current Ritual of Annihilation cost, which means that if no one has bothered to advance it then his Combat will be a pretty meager 5. I guess he at least comes with a Combat value.
At any rate his main perk is that when he fights he gets to choose where Pain and Kill results go, meaning that you can opt to, say, immediately kill an opposing Great Old One.
He Who is Not to be Named (Action: Cost 1)
For 1 Power, move Hastur to any zone that has a Cultist from any faction, and then take another Action, like Battle, Capture, or Shriek of the Byakhee (in case you want to prepare for a Battle). Note that the action doesn't have to involve Hastur in anyway, you just can't use it in conjunction with The Screaming Dead (and vice versa).
Each time a Cultist gets eliminated in the Action phase of the game, you get 1 Power right away. It won't stop other factions from gobbling up your Cultists, but at least you'll get something for it. Plus, you can replace them for free with Desecrate.
Shriek of the Byakhee (Action: Cost 1)
Move any number of Byakhee to one zone. This is great for reinforcing an area (say, after Cthulhu drops in after using Submerge), or swooping in to pick off a Cultist. It should be snagged early on, typically your third or fourth.
The Screaming Dead (Action: Cost 1)
You can move the King in Yellow and any Undead in his zone, just for the cost of 1 Power. Even better, you can take another action when you're done, allowing you to Battle, Capture a Cultist (which you can do even if there is a monster in the zone, since the King in Yellow is a Great Old One), Zingaya (see below), or even Desecrate the zone.
The Third Eye (Ongoing)
Desecration now only costs you 1 Power, and if you succeed you also get an Elder Sign. The only requirement is that Hastur has to be Awakened.
Zingaya (Action: Cost 1)
If you have Undead in a zone with an enemy Cultist, then you turn one of them into an Undead. This makes it a great combo for The Screaming Dead: spend 1 Power to move the King in Yellow and all of your undead into a zone, then spend another to use this.
Once you Awaken him, just move back to your starting zone and use Desecrate. Since you'll have six units there the attempt automatically succeeds, so you get to put down a Desecration token (+1 Power is there is at least one unit there when you Gather Power), drop a Byakhee or Undead for free, and you get another spellbook. This time I recommend Shriek of the Byakhee, or maybe Zingaya if there're some lone enemy Cultists scattered about.
Yes, you could build gates, but you want to get the King in Yellow out and about, Desecrating zones for spellbooks, free units, and even a power boost before the other factions spread out too much. You'll probably be 1-3 Power behind for the first round, but on the next few rounds you'll close the gap as you continue Desecrating zones. It's even possible that you'll come across a lone enemy Cultist, which with The Screaming Dead will be easy to Capture (or transform into an Undead if you have Zingaya).
I do not recommend sending the King in Yellow after the Black Goat or Crawling Chaos's cultists, because his Combat is 0. Yes, you could try capturing a Cultist--because Great Old Ones can capture a Cultist even if there's a monster in the zone--but if the enemy Summons a monster--or has a spellbook that lets other monsters jump in for free, like Crawling Chaos's Seek and Destroy--then there's a risk-free chance that they can take him out.
If you do feel like capturing Cultists, beware of the Black Goat, because their Fertility Cult trait allows them to Summon multiple monsters at once.
Anywho, on later rounds you're going to want to do what I call "the pilgrimage": just march the King in Yellow about (aiming for zones bearing symbols that will net you more spellbooks), using The Screaming Dead so that you only have to pay 1 Power to move your Undead retinue with you (though you'll want to leave some monsters behind, like Byakhees, to get the Power bonus).
You can do this to snap up a nearby enemy Cultist, use Zingaya to change an enemy cultist into an undead, or even just Desecrate a zone (leaving Byakhee or Undead in your wake).
Sometime around the third or forth round you should summon Hastur, namely when it means that you'll have The Third Eye and (ideally) He Who is Not to be Named spellbooks. Third Eye is likely going to be necessary to help you keep pace in the Doom point race, since without many gates you'll be lagging behind. Keep in mind that you don't need the most Doom points to win, just more than any other factions packing all six of their spellbooks.
Speaking of having all six spellbooks, an excellent tactic/nasty combo once you've got all of yours is to use He Who is Not to be Named to move Hastur somewhere, Shriek of the Byakhee to drop in support for him (more Combat dice and some cheap Kill sponges), and then Battle (which becomes Unlimited at six spellbooks). This is useful for killing other Great Old Ones, but can also be useful for taking out a Gate or weak outpost.
Finally, don't forget about the Ritual of Annihilation: you get double the Doom points and some Elder Sign tokens each time you participate, but it also boosts Hastur's Combat. Definitely do this if you have a surplus of Power and/or you end up squatting on a bunch of Gates.