I didn't bother zp-data since the upgrade instruction did not say anything about that
upload the new files :
index.php
/themes (or actually just the four official themes within - again backup if you have custom or customized themes within this folder!)
/zp-core (especially here make sure that really the entire content is replaced so that no orphaned files because of removed or renamed ones are kept)
Where are the error logs and what are they called
Keith