This is very, very early Shakespeare and it shows. The plot is that two pairs of twins have been separated at birth, with one being the master and one being the servant from each pair. Each twin has the same name as the other, so we have two servants named Dromio and two masters named Antipholus. Hilarious hijinks ensue when they end up in the same time and everyone constantly mistakes each twin for the other.
The play is out and out farce and entirely rests upon the mistaken identity gag. Its really got no subtlety to it at all and is a standard farce. The plot could come straight out of an episode of Three's Company because it is all mistakes. Its the most unsophisticated thing that I have read by Shakespeare. The language is quite pretty and the gags are good enough. However, even compared to something like Two Gentlemen of Verona it is straight-forward and relies a lot on slapstick humor. While, its perfectly fine, I certainly feel that I have read and seen things that are better. One can imagine it as an Elizabethan Fawlty Towers and that is a good comparison, because Fawlty Towers is both cleverer and funnier. This kind of thing is not really Shakespeare's forte and when he indulges in this kind of humor in later works, it is always a bit more than this and works on multiple levels. Its fine and fun, but Shakespeare at his fluffiest, safest and least original.