This post has an example of a conversation logger. It's based on the ConversationLogger.cs script included with the Dialogue System. You can probably adapt it without having to dig into C# code.
However, if you want to implement something similar in Playmaker alone, use the Dialogue System's Playmaker events. Add a Dialogue System Events To Playmaker component to your Dialogue Manager (or a child GameObject of the Dialogue Manager). Add an FSM that listens for events named OnConversationStart, OnConversationEnd, and OnConversationLine. The OnConversationLine event's string data will contain the line of text being spoken.