Are you doing it from a new thread or replying to an existing thread?
If it's an existing thread, you have to click the Quote or Reply Quote buttons, and then, like auntpiggy mentioned, you'll see the File Attachment option under the white reply box.
If, however, you're using the Quick Reply white box at the bottom of the thread page, you don't have the option to add pictures from there (and so there is no BROWSE button available). ;-)
You do have the option of adding attachments once your post has posted with the Add New Attachment option button.
Hope that helps.