The game will shift between action, during nightmares, and adventure scenes, during the daytime. Most of the adventure phase involves talking to acquaintances at the bar. During the action phases, Vincent is chased up giant staircases. If he falls from one he dies, resulting in a "game over."
The action mechanics in the game are apparently very deep, as the player will have to make choices in order to pass "stages". The game's producer, Katsura Hashino, explained that there are various ways to do this. There are three stages: Nightmare, Drama, and Stray Sheep. The "Drama" sequence occurs during waking hours, during which Vincent will choose between the two girls.
Hashino also said that "Vincent's character can change in many ways depending on the player’s choices throughout the game," and added "his character development can get pretty unusual."
The adventure segments in Catherine will consist of running around town and visiting various places.
It was stated by Famitsu that Vincent will not be alone in his nightmares and that he'll be encountering a large number of sheep. In a dream sequence the sheep, as well as Vincent, are being chased by a giant pair of hands, one of them holding a blood-covered fork.
Hashino has stated that there are multiple endings, and the first play-through of the game should last twenty hours, but in order to obtain all endings, it’ll take "up to thirty hours" to complete.
Source: Wikipedia, "Catherine (video game)," available under the CC-BY-SA License.