All admin actions, including topic ordering, require that you are signed in with an account that has admin access to the community you wish to manage.
The admin dashboard of your community can be accessed by clicking the "admin" link in the community's navigation bar.
Click Manage Forums in the dashboard's sidebar:
Click the settings icon in the forum where you wish to change the topic ordering:
Look for the topic ordering drop down in the forum features box and make your selection.
What they mean:
First post (new - old) The topics are static. They are ordered from new to old in descending order. Replying to topics will not take them out of order.
First post (old - new) The topics are static. They are ordered from old to new in descending order. Replying to topics will not take them out of order. Please note that this can be inconvenient when you have forums with multiple pages. One needs to go to the last page to see the new topics/replies.
Last post (new - old) This is the option you are the most familiar with. This is the same as the default setting. The topics are not static. New replies will move the topic to the top of the page.
Last post old - new The topics are not static. Replies will move the topics to the very back of the forum. As with first post old - new, this might not be convenient when you have forums with multiple pages.
Topic title a - z The topics are static. They are ordered from A to Z. Replying to a topic will not take it out of order.
Topic title z - a The topics are static. They are ordered from Z to A. Replying to a topic will not take it out of order.
Members can also sort the topics in a forum to suit their needs. This can be nice when you want to browse a forum that has several pages.
Click on "Topic Title" over the first column. This sorts the forum by the topic title A-Z ( numbers and special characters will be first). If you click Topic Title again, the topics will be re-sorted Z-A
Let's say that you what to look for a topic started by someone you know or you want to find a topic by a random interesting username. Click on "Author". This sorts the topics A-Z by username of the person who started the topic. Again, clicking again resorts Z-A
If you click on "Replies", the topics are sorted by the number of replies the topic has, starting with the most replies down to the least. Click again to reverse the order.
"Views" and "Points" work the same way.
"Last Post" sorts by the date/time stamp of the last post in the topic. If the forum is set for default ordering, the most recent post will be at the top and clicking last post will re-order so that the oldest topic is first. If the board has the ordering for the forums set another way (such as A-z), then clicking once puts the newest first and the second click puts the oldest first.