For each media asset type, there may be custom attributes and fields you'll want to set.  At the very least, the alternate text or caption fields for images should be filled in.  (Note:  Media module version 7.x-1.x does not have built-in ALT Text properties, the caption is sometimes used as a workaround to populate the ALT Text field).

From the grid view of media assets, you can click an item to open it's edit form.  From the list/table view, click the "Edit" link to open it's edit form.

Below is a sample screenshot of an edit form for an image.