Are you trying to connect via Wi-Fi? Make sure you know the Wi-Fi password or you are not filtered from connecting. But if you are trying to connect via O2's network, simply follow these:
Open Settings > Wireless & networks > Mobile networks > Access Point Names
Enter the following:
Name: O2.ie Internet
APN: internet
Proxy: leave blank
Port: leave blank
Username: blank
Password: blank
Server: blank
MMSC: http://mmsc.mms.o2.ie:8002
MMS Proxy: 62.40.32.40
MMS Port : 8080
MMS Protocol : WAP 2.0
MCC : 272
MNC : 02
Authentication Type : PAP
Let us know if you are able to have internet on the phone after following what I posted above. :)