Just visit www.google.com/talk from your iPhone or go to this page and enter your mobile number there. Google will send you download link on your iPhone directly.
If you like new Google Talk interface for iPhones, then you can use its Google Talk Gadget version from your browser, specially from Firefox sidebar, thanks to Amit Agarwal. Just use the following links.
For Google Accounts / Gmail users:
For Google Apps:
Till now Google Talk client was only available for Windows based operating system. This launch came as a little surprise to me as I am waiting from long for an official Google Talk client for Mac OS.
I use Adium on Mac for chat but it doesn’t support Google Talks invisible status feature, which I need more often than any other feature.
Thanks for tip Martin.
Link: Google Talk for iPhone