In the morning after you meet with your idols in the office, you get a choice to talk with one of your idols. This conversation, which primarily affects your idols' mood, is covered under Morning Greetings.
Before an audition, live or festival, there is a brief communication segment where you will cheer with the idols. This is covered under Cheer.
Communication during promotions and publicity is covered under Idol-Specific Communication.
At the end of each week of play (aside from some weeks, where other events occur instead), you get a chance to talk with your idols before they go home in the evening. This is an optional segment and if you choose not to do it, their mood will remain exactly the same.
If you do choose to do it, there is a risk. If you fail, it does ruin their mood but if you succeed, it is an effective way to boost it.
The choice you get each week:
(X on 360): Deliberately say something. (じっくり話をする)
(B on 360): That's it for today. (今日はこれにて)
If you choose to do it, the game will be randomly selected from one of the four possibilities: