in my experience of administering a vBulletin site, you have to 'attach' the image, rather than embed it in your post.
To do this, click the reply button (not the quick reply box at the bottom of this page) and then click this little paperclip image:

.
A popup should appear with the option to 'Upload file from your computer'. Just keep in mind that the site probably has restrictions on image sizes.
It won't appear as an embedded image, it'll appear as an attachment at the bottom of your post. If you want to embed an image, you'll need to host the image online somewhere. Or some vBulletin sites have a picture gallery included. Haven't seen one here.
Hope that helps!