Since Krark-Clan Ironworks was banned from Modern, Dredge has been my deck of choice. I'm an easy sell on a Faithless Looting deck, since I think it's better than Brainstorm in Legacy, and Creeping Chill is incredible in Dredge. Creeping Chill is also particularly well-positioned in Modern right now. Dredge is like the unfair version of Martyr or Soul Sisters – if your opponent is primarily concerned with your life total, you probably have a good matchup. If your opponent routinely does damage in increments of more than ten or doesn't really care about your life total, you're a lot more likely to have problems, particularly if they're very proactive. Where Dredge performs better than other lifegain decks is against reactive strategies, which usually don't have enough of the right kinds of reaction.
What this means more precisely is that Dredge is great against Burn, Grixis Death's Shadow, Izzet Phoenix, Azorius Control, and usually most creature decks, and bad against fast combo decks – Amulet Titan, Tron, Grishoalbrand, and Selesyna Hexproof. It's close against decks that are in the middle, like TitanShift and Hardened Scales.
Almost any specific player can give their deck a good matchup against Dredge if they want it badly enough, but that's not really how Modern works. Modern demands that players be able to interact with the graveyard, but they have a lot of other needs in their sideboard as well, so they can't usually play that many cards that interact with the graveyard and not all graveyard hate is the same. Additionally, Dredge has a lot of counterplay, so I don't really consider the amount of hate Dredge currently faces to be particularly daunting.
The first stage of the game is mulliganing, and Dredge mulligans a lot. I hate keeping any hand with only one land unless it has a Faithless Looting, and I rarely keep hands without either Faithless Looting or Cathartic Reunion. I'll make an exception for hands with two or more lands with a green source and two Shriekhorns, or maybe hands with a Shriekhorn, a Life from the Loam, two lands with a green source, and good other spells (especially looking for no Narcomoeba). I also wouldn't want to keep a hand with Cathartic Reunion and no Dredge card. This is all somewhat demanding, but as long as you have a good start, it really doesn't matter how many cards are in your opening hand, so I'm not that scared to mulligan to five cards.
Playing the games after that is pretty straightforward, but here are a few tricks and tips: