"Ever Their praises, and abundance to the Black Goat of the Woods. Iä! Shub-Niggurath! Iä! Shub-Niggurath! The Black Goat of the Woods with a Thousand Young!" - from The Whisperer in Darkness.
This monsterous faction, led by Shub-Niggurath herself, finds allies in ghouls, dholes, Mi-Go, dark young, and all manner of creepy crawly terrors that live under the earth.
Dark Young specialize in rapidly reproducing. You can see this in Hungry Dark Young, who can bring a friend along with him when he enters play, or Ferocious Dark Young, who won't rest in the grave when he hears his brother enter the battlefield.
Mi-Go specialize in buffing each other. If you can make a deck focusing on bringing out multiple Mi-Go, each makes the others stronger, until you have an army of creatures stronger than Ancient ones. Mi-Go Scout grants each Mi-Go a clue icon, each Mi-Go Surgeon a book. You can rapidly stack Mi-Go to scatter toughness(Ageless Mi-Go), combat(Mi-Go Commander), or whatever else you need to ever Mi-Go you have in play. Add a Specimen Room and they can dominate the skill challenge as well.
Ghouls specialize in being strong for their cost, but scared of the dark. With Ghoulish Predator, you pay 2 resources to get a terror and combat icon, toughness +1, and a whopping 4 skill. The downside comes when he can't commit to stories during the day. Ghoulish Hag refuses to stay dead, being able to be played even from your discard pile if it's night, but day destroys him outright.
Shub can stand very well on it's own, due to a strong combitation of terror and combat icons. They have a good mix of lower and higher cost characters. Shub also brings strong Event cards to the table. As long as it's night, Back From the Dead lets you steal an oponent's character out of his graveyard, opening up all sorts of unique combos without having to invest in that faction. Shocking Transformation is another sneaky way to get a character into play, and doesn't require any faction investment in resources. Even if you stick with a Shub card, having 6 chances to draw to a vital card instead of 3 is a huge advantage. Unspeakable Transformation can throw a monkey wrench into your opponent's calculated plans and let you bring extra icons where it'll hurt the most.
You'd expect a mythos faction to be low on clue icons, and generally Shub is, but they're also very light on book icons. This can make a shub deck play frusteringly slow, having to hold back characters in the early game so they're available to defend. Generally you're only going to see one skull icon per character until you get to the heavy artilery, so Shub can definitely be outgunned and shot down by a faction like The Agency.
Night or Day?
If you're looking to play with Shub's ghouls, you'll absolutely need to commit to night, or risk having your monsters crippled by a single card. Dark Young and Mi-Go are much more agnostic, so if you focus on those subfactions you don't need to worry about it quite so much.
Low Cost Wonders:
Shub packs a brutal opening game. With the right draw luck, Turn 1 you can bring out a Gibbering Soul, and attach a Eat the Dead to him. With your final domain, play a neutral Diseased Sewer Rats, allowing you to wound your own Gibbering Soul. The results? On Turn 2, you have a 4 resource domain, with a heavy hitter (may I suggest Y'Golonac?) ready to play.
Y'Golonac is an modestly priced beast with invulnerability and an Action that makes it easy to force your opponent's characters into bad matchups. Dimensional Worm has a fun ability to mix up the story, but you'll need some help to bring the book icons. A Clever Zoog might do the trick. With Shub's ability to build up resources, Slavering Gug can deal massive wounds from a safe position in the end game.
I've had good luck with a Christmas deck (Cthulhu and Shub together), but typically if I play Shub, I like to play it mono-faction. With the multiplicative power of the Mi-Go, every non Mi-Go card in your deck seems like an oppurtunity wasted.