I’m trying to remember – is there a ‘Save for Web’ option in 6’s File menu? If so, once you have created your slices, select this option. Now use the Slice Select Tool to select the slices you want to export (drag select to select all).
Select the image settings you need in the far right bar. Click Save.
You will see a ‘Save as type’ option where you can opt to save just the image slices or the slices and an html page. The latter is a good option if you are taking them into Dreamweaver as you can just open the html and they will already be laid out in a table.
If you select ‘Other…’ in the ‘Settings’ option you will be able to set a number of options pertaining to your saved images and html file.
Once saved, open the html in Dreamweaver or Insert the slices. Sorted!
I’d recommend doing this through ImageReady even if you made your slices in Photoshop. ImageReady has an optimize palette that will let you individually set each slices output settings (GIF, JPG, PNG, quality, etc.) Once you do this go to File -> Save Optimized As… then choose a location for the files. You can also save an HTML file that recreates the images within a table and set image name conventions amongst other things. Make sure you choose All Images in the last drop down on the save dialog box.
Be aware that a sliced image cannot be used as a background in web design.