As we said, it need not be an earthshattering story in order for us to relate it—it can short episodes of Hashgachah Pratis, and so on. "Do you know what happened to me? I was waiting for a parking spot, and I davened, and soon I found a spot!... "Do you know what happened? I was looking for something, and I said Amar Rabbi Binyamin, and I soon found it."
This type of chatter can sometimes be more effective that formal speeches. Because, when a person sees that another person is preparing to relate something formally, their guard goes up. They can become skeptical... whereas in informal conversation, people can sometimes more readily accept what is being said—it seeps into their heart more easily. Thus, our Shabbos "conversations" can be an incredible opportunity to convey emunah and bitachon in Hashem to our children.
The Rambam (Avos 1:17) divides speech into a number of categories. There is speech of mitzvah, speech of aveirah, and then there is speech called הנאהב דיבור, speech that brings a person to love Hashem—such as speech that lauds the good and denigrates evil.
Thus, the child's perceptions and attitudes—what is fitting and what isn't, what is good and what is not, etc., are largely shaped by our words during the seudos Shabbos. If we engage in conversation that denigrates other people, chas v'shalom, our children will get the idea that this is appropriate conduct.