Without knowing the version of Joomla! you are dealing with, it’s hard to say what is happening (there are a lot of settings to be tweaked, and broken, in Joomla!).
When editing an article, look in the lower left hand corner of the Joomla Aricle editing sreen for the “IMAGE” link/buttom (to the left of the “Page Break” and “read more” links/buttons"). Click that and a “light box” effect will pop over the editor, and there is a “browse” button in that!
–DreamHost Tech Support