All dialog events are in the following format:
on *:dialog:DNAME:DEVENT:DID:{ ...code here... }
Where DNAME, DEVENT, and DID are the dialog name, event, and control ID, respectively. The mIRC helpfile gives a list of all the dialog events that are possible; but in your case you'd want to use this:
on *:dialog:game:sclick:2:{ msg $me Hello, are you there? }
This means "On a dialog event, when the user single-clicks (sclick) on the Message Me button (2) in the dialog (game) then send myself a message.