There's now 5 seasons of the show, which makes it pretty tough to summarize, but I'll try. The show is about "the Gang," and their shenanigans. The episodes are largely self-contained but there's quite a few running jokes and the show will generally seem less inexplicable if you realize going in that all of the characters are incredibly selfish and are about as loyal as socially maladjusted vultures. They are constantly betraying one another over money, sex and petty slights. Much of the show takes place in a poorly ran bar (Paddy's) owned at various points by several of the characters.
A quick run down of the 5 primaries:
Dennis: Vain, stupid, drunken lech. Dee's twin brother.
Deandra, aka, Sweet Dee: Drunken, stupid black sheep. Target of rampant sexism and receives little to no respect from the rest of the cast, even from her twin brother. Bartender at Paddy's. As far as I'm aware, she's the only one never allowed to become a co-owner of the bar. Her ideas are routinely dismissed by the other characters only to be adopted later with no credit being given to her.
Mac: Vain, stupid, drunken hypocrite. Likes to act the tough guy and usually gets his ass kicked for it.
Charlie: So stupid the rest of the cast thinks he's stupid. When he's not drinking he's sniffing glue. Freakishly durable. Has a crush on The Waitress and lives in squalor.
Frank: Only introduced after a few seasons. Played by Danny DeVito, he is Dennis and Dee's legal but not biological father. Lives with Charlie (who may be his biological child) despite having a surprising amount of wealth and illegal connections. Often gets the best of other cast members through experience, but is still mostly stupid. Often is gambling or otherwise mixed up in shady deals. Last I checked he is the primary owner of Paddy's now.
Other important characters:
The Waitress: works at a coffee shop. She's obsessed with Dennis, who isn't interested, and Charlie is obsessed with her, so she often ends up getting involved in whatever stupid shit is going on from episode to episode.
Cricket: A homeless guy who suffers greatly at the hands of the Gang. Former priest who wouldn't be homeless if it weren't for the main characters. Dennis and Mac teabag him constantly. He is attracted to Sweet Dee.