To post a clip, do the following:
Click either the "New Thread" (if making a thread for the clip) or "New Reply" (if posting the clip in an existing thread) as normal to bring up the screen with the box to type your post in.
Scroll below that box, below the Submit Reply and Preview Post buttons. See "Attach Files" in "Additional Options"? Look for a "Manage Attachments" button. Click it.
A window should pop up. To upload a file from you computer simply hit one of the "Browse" buttons next to the white boxes and then find the clip on your computer. Once found click "Open" in the file browser. Text should appear in one of the boxes. Repeat for additional files (Up to five) by using the other browse buttons.
To upload the file, click the "Upload" button next to the "Browse" buttons. It will take time. Eventually the view will change with the name of your uploaded file appearing as a link. If it does not work, scroll down and check the allowed filesizes for the file type you are uploading. If it is bigger than the limit for its type then you will have to split it or shrink it.
Once done uploading, close the little uploading window. Finish typing your post if necessary and post as normal. Your attachment should be there.