Google now allows you to chat on Google Talk via iPhone without even downloading it. Simply open your iPhone Safari browser and launch http://www.google.com/talk in order to be able to use the messenger and chat to your friends in real time.
Alternatively, you can always download a personalized app for Google Talk, in case if the above method does not work, you should not have any issue. You can do this via the iPhone’s App Store and Google Talk will be available for a free download there.
Simply open iTunes and look for Vtok - Google talk, which is a free app. Once it is downloaded, transfer it to your iPhone and launch it. In case you are unable to search for it properly, try using the Search option in your iPhone which is available on the left side of your homescreen.