Here is a quote from Ventara on NeoGAF describing Danganronpa 1:
The premise is that you are starting at a new high school, but things take a bizarre turn when you and 14 other students end up locked in said school and are trapped in their to live out the rest of your lives. The only way to get out is to murder someone without anyone finding out. You don't know who is behind this or why they're doing it, just that an annoying robotic toy bear called Monokuma is the one relaying all the info to you, and you need to watch your back since everyone has a motive to kill, since that's the only way to get out.
Gameplay plays out in three parts per chapter. First part is story/finding dead body, second part is investigation/point-and-click as you move around the school in 3D (very rudimentary), and the last part is the trial/mix of mini-games. During the trial, you try to uncover the truth by pointing out lies in statements. You do this by taking one of the facts (or "bullet" points) and "shooting" the part of the statement that's contradictory. There are some other mini-games during the trial like hangman and a rhythm game, but they essentially serve the same purpose.