There are two ways for the iPhone to get it's Zimbra connection.
The simplest it to just use th IMAP capability that nearly any normal email client can do. That would be email and email only.
The second option requires that you have the Zimbra Mobile option on you Zimbra Network Edition. Sync and backup all settings on your phone first, including your contacts just in case. On the iPhone (2.0+ software): Settings > Mail, Contacts, Calendars > Add Account... > Microsoft Exchange. Thisi s the top option when you set up a new account. Feed it all of your Zimbra information and it's quite easy.
If you choose to sync your contacts, be aware that you will wipe out your contacts on the phone and replace them with what is on the server. I figured out a way to get both to mesh up here: iPhone Contact Sync/Merge
Mail | Dell 2950III | 2x Quad Core 5420 | 8gb RAM | 6x 146gb SAS RAID 0+1 | Red Hat 5.3 | Zimbra 6.0.10 Network Edition
Test | VMware ESXi Whitebox | Phenom II Black 3.2ghz | 12gb RAM | 6x 1tb SATA RAID 0+1 | CentOS 5.4 | FOSS, Not in use now