Private Chats
Private chats can be triggered if your Friendship rank is at least LV3. To do this, you have to find the party member or friend that you want to have a private chat with, press Square for the menu to appear, then select "Go for a walk". You can then bring your partner to different dating spots in the game and trigger private conversations with them. There are a limited amount of times you can have private conversations with different characters; to "reset" them, you have to sleep in the inn, temporarily split up with your partner/date, or spend some time away exploring. There are several dating spots in the town and you can bring your partner to trigger private chats once per session.
Private chats is basically a mini-game to increase the affection level and mood of your partner towards you. During the conversation, you'll see various options to lean closer, move away, nod, or shake your head. Your objective to provide the favorable response (nod or shake your head) to your partner's questions. You won't be making any audible responses aside from nodding and head shaking so you have to time your answers properly.
Your objective in the mini-game is to keep the beating heart icon in the "sweet" red spot. As you lean closer, actions become available ranging from innocently mild ones like gazing intently to more sensual ones like touching the waist and kissing. The color of the heart changes as well, which corresponds the character's comfort towards your approach. If you see the heart turn purple, your chances to "fail" in getting a positive reaction from your partner is high. If it is blue, there's a chance that your partner's mood will worsen and she'll prematurely end the conversation. If you’re able to maintain a good conversation with her, you’ll get a popup message that will tell you how much “points” your friendship has improved or if you and your partner had a good time.
Aggressive Private Chat Trick
There’s one effective but aggressive trick that will allow you to maximize the mood of your partner per private chat. (Credit for this trick goes to the Gamefaqs forum) What you need to do is at the very instant that the private conversation starts, zoom in (lean forward) to get close to your partner, ignoring the blue heart and keep pressing square to perform all the action prompts until you reach the last action, Kiss. After landing the kiss, zoom out/ pull back enough to get back to the purple colored heart and stay there. Now you can stick with the conversation and gave the favorable responses to keep the heart beating fast and in red. When done correctly, this should greatly improve, even maximize your partner’s mood while also giving you a solid amount of friendship improvement points. The amount of points you’ll get will still vary on how good your responses are. The videos below will show you how to do it.
Mood Changes and Pillow Talks
If you're able to maintain your partner's good mood, you can hold her hand and stroll slowly in town. Furthermore, you can bring her to your room in the inn, hold her hand, then princess carry her to the bed. If you're able to princess carry her at all, then you should be able to trigger a Pillow Talk sequence.
The Pillow Talk is a special private chat where you can further improve her overall mood. (You can still use the trick mentioned above). Unique characters in the game like Asuna, Strea, and Leafa have special CG sequences that will serve as your eye-candy reward for successfully convincing a date to sleep with you in the inn. For other characters and NPCs, the screen will just fade to black without a CG sequence. You can refer to some of the pillow talk videos below.