Not much different from the pronunciation of "s". Im sure many Dutch teachers disagree with this (there should be a slight difference), but thats for advanced practitioners

In Dutch, when pronouncing a “z”, the position of the mouth and the tongue are exactly the same as when pronouncing a “s”. The only difference is that vocal cords should vibrate while pronouncing a “z”. I agree with Jelmer that the s and the z more and more tend to be pronounced the same (like a s), but i think it is nicer when the vocal cords are used, at least a little bit.

I tend to disagree with the other answers. Zwolle really sounds different then swolle. Maybe it's hard to differentiate in some regions or dialects? For example: liseten to Zwolle pronounced in dutch: http://www.forvo.com/word/zwolle/ and Zevenaar: http://www.forvo.com/word/zevenaar