There are many ways to do it. Basically you need to store posts and display them in a nested format, meaning that you should pull down the data and then nest it based on child-parent relationships.

I wrote something similar in golang. An example is http://askgolang.com/ and the package itself with demo code is at https://github.com/carbocation/go.graf

Of course, this can be done in any language, but I found to quite pleasant (and safe).