We are at the beginning of a very special period in the year: the nine days. These are the days from the beginning of the month of Menachem Av until the 9th of Menachem Av, which marks, so to speak, the saddest day of the year, when we fast for the great tragedies that have befallen the Jewish people throughout history.
In general, the Jewish view of history is that it should serve as a guide for the path of the future. This is reflected in the words of our sages: "The actions of our patriarchs are signs for our children." These words refer specifically to the stories the Torah records about Abraham, Isaac, and Jacob, our patriarchs, which we see repeated in the stories of later generations. Thus, we learn from them how to deal with the difficulties that arise throughout history.
In a similar spirit, we find in the customs related to these days, and even more so in the fast of the 9th of Av (Tisha B'Av, July 29th this year): the study of what happened, the preparation during these days, and the fast itself serve to introspect and analyze in reverse: those events that led to the tragedies of the 9th of Av teach us what work we must do to reverse them. In other words, the causes that led to the exile of more than two thousand years determine, in a way, the method for emerging from exile.
Our sages explain that the First Temple was destroyed because the Jewish people showed no respect for the Torah. The Second Temple was destroyed because of the unfounded hatred among the people. In a more general and comprehensive way, the Men of the Great Assembly, who determined and established (among other matters) the liturgy of prayer, decreed that we say in the Musaf prayer, which replaces the additional sacrifices of each festival: "For our sins we were exiled from our land.".
Regarding the last point, the concept of sin can be understood as a failure to observe a mitzvah, whether positive (not performing it when required) or prohibitive (doing something that should not have been done), or as negligence in the level of observance a person could have achieved. In this latter sense, sin means that more was expected of the person, despite not having done anything wrong.
Regarding the cause of the destruction of the Temples, it is clear that the way to counteract these events is with an addition to the study of Torah in general and in particular of the deep part of the Torah, Hasidic philosophy, which leads, among other things, to appreciating the sanctity of the Torah and the greatness of its Giver, and also with an addition in love for one's neighbor.
Regarding the liturgy of our sages, the main thing is to begin to improve; each step a person takes is an advance, a way of transforming "we were exiled from our land" into "salvation will be for God.".