You have to set the type of file you want to save in the optimize palette (GIF or JPEG). Then you need to export the image - Fireworks will still save a PNG (this is the file type that FW uses to maintain editability), but it will also save the new file to a folder of your choice.
Of course if it is just a small part of the image that you want to save you need to insert a slice first, then select the slice and go through the same procedure, or right click on the selected slice and choose 'export selected slices'.