"Oh, there ain't no rest for the wicked, money don't grow on trees. We got bills to pay, we got mouths to feed, there ain't nothing in this world for free. I know we can't slow down, we can't hold back, though you know, we wish we could. No there ain't no rest for the wicked, until we close our eyes for good" - Cage the Elephant
The Syndicate represents the underworld portion of human society. Thugs, mobsters, petty thieves. They don't particularly care if the humans or monsters come out ahead in their struggles, so long as there's a buck in it for them.
Syndicate shines as a "helper" faction. They have myriad event and support cards to bolster your characters and frusterate your opponent's efforts.
Here are some examples of what you can do with a combination of Syndicate Event and Support cards:
Debuff and exhaust opponent characters - Kidnapping 101 allows you to remove an opponent's character from a story. Since it's an event, you can wait until he commits his characters and then spring it on him, choosing where it'll hurt most to wreck his carefully calculated plans. Bound and Gagged allows you to blank a character, and prevent it from committing to stories. This can be very useful against a low cost character with a useful Action, or against a character your oponent was intending to use as a sacrificial lamb (say, with Shub's Eat the Dead attached). Panic allows you to mass exhaust characters, and you can choose the perfect time to play it (just before you refresh your characters). It also grows more powerful as the game progresses and you have domains with additional resources.
View your opponent's hand - Seeing your opponent's hand can save you from nasty event card surprises, and help you plan your strategy in advance. Eyes in a Jar allows you to always see your opponent's complete hand for only a cost 2, this is a very powerful support card for its price. Alternatively, you can play A Sight for Sore Eyes, paying only 1 for a one time peak at your opponent's hand, with the potential bonus of a nice skill boost if you can guess what cards he might have. Another card easily worth the cost to play.
Draw Additional Cards - Want Ads allows you to draw 2 cards, as long as you can reliable manage to get your opponent's character into the discard pile. The Laundromat gives you a Support card allowing you to get a constant stream of new cards, as long as you can pay the cost 2 each.
Have an additional cache of cards on the bottom of your deck - Both The Laundromat (mentioned above) and Smugglers allow you to get cards to the bottom of your deck, waiting until they're useful. You can then use Smugglers ability, or a card like Bootlegging Operation to retrieve them when they're needed. Even if you've gone through the cards you've deliberately placed there, it's still useful to draw cards from the bottom randomly if you need cards to use.
Syndicate characters tend to be underpowered. They're not completely worthless, and you can cherry pick some gems, but in general you're going in very light on icons. Rank and file Syndicate members are typically susceptible to terror, lacking both terror icons and willpower. Once you get to the expensive Syndicate characters (cost 4+), you can generally get a good combination of skull, book, and clue icons, with Willpower thrown in. You do need to watch out for characters with double edged swords that can actually hurt you. Blackball Jim has an effect that can potentially help or hurt you, but as least you have some control over how it plays out. The Back Room, on the other hand, costs you 2 to play, and provides your opponent the same benefit you receive. Unless you have some reason to think you'll make better use of the drawing, you're paying for no advantage to yourself. As a worst case, Clover Club Regular allows you to see the top card of an opponent's deck (useful), but allows him to draw a card every time he places a success token on a story. This can quickly get out of hand, backfiring and giving your opponent the resources he needs to beat you. I'd recommend using a neutral Dreamlands Eclipse instead, and not giving your opponent a card advantage.
Night or Day?
Syndicate has almost zero perference if it's Night or Day. This comes in handy since you'll typically be using them as a buddy faction to another faction, so whatever the other faction prefers you can go with (or simply ignore Day/Night if you prefer). The one exception I can think of is Gregory Gry, who gains a nice bonus if it's Day.
Low Cost Wonders:
Tattoo Artist can be very useful in the early game. If you can use her ability to reduce the defender's overall skill to zero or below, you can claim 2 success tokens during the skill challenge instead of one. Hard Case is a decent cost 2, with the criminal subtype, who can help turn the tide early by exhausting an opponent and allowing you to run unopposed. Brazen Hoodlum is another cost 2 criminal who can nullify an opponent's skill and get you extra success tokens early.
King Kuranes is a solid cost 4, bringing a mix of skull, book, and clue icons, along with willpower. His Response, allowing you to take control of Dreamlands Support cards, can be absolutely brutal against an opponent using them, since often they can only take effect if you control more than your opponent. Dr. Marinus Bicknell Willet isn't a bad choice for cost 4, adding Fast on top of the typical skull/book/clue/willpower combination. Richard Upton Pickman is a terrific cost 4 character. He can pay 2 to steal an enemy character's keywords and triggered abilities, leaving that character's box blank. This can allow you to remove nasty characters you couldn't otherwise, for example stripping Y'Golonac of his invulnerability and forcing him to face you in his weakened state.
Syndicate can easily work with any other faction, providing a great support base and allowing the other faction's characters to shine.