Copying this here from a Reddit question about how the Dialog Grid works:
Its very similar to the hexflower in Pettish (on itch). I like to treat dialog as a mini-game. Whenever you start a conversation with an NPC, start on the center square "Fact", say what you want to say to the NPC, then roll 2d10 to determine their response.
The first d10 specifies the direction on the grid to travel, and the tone of the response. The second d10 specifies the subject/target of their response. On doubles, the NPC ends the conversation.
So for example, lets say I ask the merchant if there are any discounts on swords. I roll 2d10 and get 2,0. The 2 means I move up one square, from "Fact" to "Need", the tone of the response is "Neutral", and the subject is "Us" (from the 0).
Oh, also, the top two rows, in italics, indicate that the response is related to the past, while the bottom 3 rows indicate that the response is related to the present.
So this merchant's response is neutral, about something they need, something from the past, and about "us" (from the perspective of the merchant, perhaps the merchant's guild or something).
You could then interpret this however you wish. Maybe they are low on stock due to monster attacks on the road, making it hard to order new supplies. I generally like to try and spin it into a sidequest of some sort.
If you continue the conversation, have your character say what they want, then roll 2d10 again, and move from the "Need" square to the next. For example, a roll of 8,3 would right shift to "Query". This means the NPC would aggressively ask a question with a subject of "me" (again, from the perspective of the NPC, literally him). For example: "What am I supposed to do??"
Continue as long as you wish (or until rolling doubles), flushing out the dialog to introduce hints, lore, quests, or whatever into your world.