Push Gmail for the iPhone lets you get new e-mail messages delivered to your iPhone more quickly. But the feature isn't built in to the iPhone; you need to use Google Sync to get it. Here's a quick guide that explains exactly how to set it up.
Before you begin adding Google Sync to your iPhone, you should backup all of your data.
You can backup your iPhone using iTunes. Connect your iPhone to your computer using its USB cord and open iTunes.
You need to be running version 3.0 or higher of the iPhone OS in order to run Google Sync. (You can check which version your phone is running by going into Settings, then General, then About, and then Version.) If you're not already running version 3.0 or higher, you can update it while your phone is connected to iTunes.