Google Talk uses XMPP (Extensible Messaging and Presence Protocol). You can use for example the XMPPFramework framework to implement it. This framework is listed on a XMPP Foundation website.
XMPPFramework provides a core implementation of RFC-3920 (the xmpp standard), along with the tools needed to read & write XML.
Check out the Getting Started Guide for iOS. It contains an example iOS project.
Furthermore, have a look into Google Talk Developer Documentation. There is a section called: I want to build a client that connects to the Google Talk service which describes steps you should take to implement a client.