If you want to see the threads with the most recommendations in the last 24 hours, and the newest threads that are getting recommended, visit the Greatest page:
https://www.democraticunderground.com/?com=greatest_threads
If you want to see the newest threads that were started in chronological order, visit the Latest page:
https://www.democraticunderground.com/?com=latest_threads
If you want to see threads with the most replies, click the "Most discussed" button at the top of the Latest page to get this view:
https://www.democraticunderground.com/?com=latest_threads&mode=latest&sort1=replies
If you want to see the threads which were most recently replied to, click the "Last replied" button at the top of the Latest page to get this view:
https://www.democraticunderground.com/?com=latest_threads&mode=latest&sort1=lastreply
Note that you can also use the filter bar at the top of the Latest page to change the timeframe that you would like to see threads from, which means that you can see the most recommended threads from different time periods other than 24 hours, by clicking the "Most rec'd" button to get this view:
https://www.democraticunderground.com/?com=latest_threads&mode=latest&sort1=recs
If you want to see active, ongoing discussions, visit individual forums such as General Discussion:
https://www.democraticunderground.com/?com=forum&id=1002
In a forum, the most recently-replied-to thread is kicked back to the top of the forum, so threads which are under active discussion will appear at the top.
If you see a thread which interests you and you want to come back to later, bookmark the thread using the button at the bottom of the OP and then check back to it later using your Bookmarks page (link found in the top-right page navigation):
https://www.democraticunderground.com/?com=myaccount&sub=bookmarks
And FWIW, the still-in-development DU4 will improve upon all of the above functionality and includes new ways to sort and locate threads.
= new reply since forum marked as read