Well, this is a really hard thing.
I like to teach this as an empathy-related social skill set as much as anything else. That kind of conversation can start with questions like:
"What kinds of things make you feel good about yourself? Are there things that you aren't so happy about? How does it make you feel when {person the child knows, preferably a peer} talks about their prowess/superiority at/with {area that the child is insecure about or struggles with}? Does it make you feel like you want to talk with him/her? Or do you want to stop talking to him/her? Why? Do you think that sometimes other people feel that way when you talk about yourself? How can you make them feel better about your conversation with them without lying?"
The other part of this is about social BOUNDARIES with friendly strangers. After all, there are a good many things which aren't necessarily appropriate conversation starters with strangers simply because they are more privileged information about us; no time like the present to build awareness about being circumspect about our personal information, right??
"What kinds of things are good ways of holding a conversation with a friendly stranger? Do they need to know {fill in with a variety of things that your child COULD talk about which are true}? Are there some things that we share only with some people? Why? What kinds of things do adults like to talk about with other adults who are strangers to us? What do adults seem to like to talk about with children? What things do you think that Mom and Dad don't talk about with strangers? What do you think our reasons are for not talking about {our house payments or medical bills, etc.} with most other people we know?"
I'm also fairly fortunate in that my DD seems to have a social awareness and empathetic skill set which is kind of freakishly good, so she has ALWAYS managed to avoid this kind of thing for the most part. We've had to encourage her that it is really okay to answer direct and specific questions honestly. She tends to be extremely evasive, to the point of erring on the side of weirdness sometimes in her effort to evade such things. She immediately evaluates whether the person talking has a reason to know her age or her grade... or is more likely to assume older or younger (chronological) age, and then she does everything in her power to confirm their impressions.
LOL.
