Not sure you have to display anything on the site itself. It would be good practice to show how you deal with private data and PII.
In terms of what your obligations are - you are obliged to securely maintain personal data - i.e. not to share or use that data outside the terms under which people have given you that data. You may also be obliged to grant access to any data you store in electronic format to the 'owner' of that data - i.e. if you have a record on me I believe I have a right to see what that record holds.
You're best bet here though is to visit the website of the Data Commish - lots of guides over there:
Home - Data Protection Commissioner - Ireland