This is an article published in 1997 by Aron et al., where they developed a procedure for to generate interpersonal closeness, aptly named the "fast friends" procedure. Here is the abstract:
The questions used are available in this article in The Guardian:
What I find interesting about it is that the key to these procedure is to promote self-disclosure, talking about things that are important for people's identity in a non-threatening way using silly questions (e.g. When did you last sing to yourself? To someone else?). And it does so in a progressive way, starting with questions that require lower levels of self-disclosure and eventually getting into more personal questions (e.g. When did you last cry in front of another person? By yourself?).
I think it shows how easily we can like other people given the right conditions, and how important self-disclosure is for friendship development (there is plenty more research on that). Also, the importance of starting slow, but progressing steadily throughout a conversation.