How do I know if someone has responded to the thread that I posted?

Go to the menu 'Quick Links' in the purple menu bar.
In the drop down menu you will see 'My Posts' & 'My threads'.
Clicking on 'My Posts' will show the preview of all the individual posts you had made.
Clicking on 'My Threads' will show the listing of all the discussion threads you started.
Further click on the title of your post (from the preview) or the title of your thread (from the listing). This will take you into that specific thread.
Scroll through the thread to see postings (if any) by other members.

Note: You can also subscribe to the thread you started, that way when someone responds to the thread you will be automatically notified via email by the site. Refer this - How can I get notified when someone responds to a thread of my interest?