Bigdog. It is very easy, at least from a browser. When you select the Reply to Thread or Reply With Quote button, a window is opened (as it is for me now). Type text (if you want to precede the video with text) and when you have the cursor at the position where you want to insert the video, select the "insert video" icon (it looks like a movie reel) that is displayed above the text window (on my screen it is in the 4th box of icons in the middle row for the 3 lines of icons) The "insert video" icon is the one on the right of that box. A box will pop up that allows you to enter the URL of the video (YouTube etc) and when you hit OK the video will be inserted at that point. You can add further text after the video if you like.
It doesn't seem to allow you to upload your own videos as it only accepts a URL, not a file on your system. BTW, if you hover the cursor over each icon, it will tell you what they do.