@Theaetetus,
To enter into an existing discussion (thread), you need only write your comments or questions in the box immediately below the last post. When you are satisfied with what you have written, you can simply hit the Quick Reply button in the row of blue boxes in the last post.
If you want addition formatting options, then you can hit the Post Reply button BEFORE typing in your response.
The Thank You blue button at the bottom of each post, at least here, is a way of thanking the poster for his or her contribution to the conversation, and does not imply agreement with the opinion or position expressed. These thanks are accumulated for each Member and increase the Rep Power that appears across from each Name.
To quote a previous post, highlight only that part of the text you want and then copy/paste it to your text box. Then highlight it there and hit the Quote Icon; you will see formatting codes on each side of the text that will show as a box around it when you actually post your reply.
I hope that helps you, and as Theaetetus has written, never hesitate to ask questions or for help.
Regards,
John