How do you let a soul go on elder scrolls 3

You cannot 'free up' any of the standard soul gems - you can only use them, and the act of using them for any purpose, will consume the item completely.

If you're talking about Azura's Star, there's still no way to 'release' a soul from it, but if you use the Star for any of the usual purposes, you'll keep Azura's Star afterwards and it will now be empty.