Most likely your iPhone will tell you when a software update is available. Alternatively, you can get iTunes to check regularly or force a check (by clicking the "Check for Update" button as you see here)...

Or (as in the example below) you are likely to need to update the software the first time you connect it to your computer to activate it. So let's start there...

Connect the USB dock connector cable into the bottom of the iPhone 3G. Download iTunes and install it if you haven't already. Launch iTunes and then plug your iPhone 3G into your computer. In the iPhone section of iTunes, find the "Summary" tab and click on the appropriate button

In the example above, the iPhone was plugged in for the first time and before it could be registered, iTunes indicated an update was available. Click on "Download and Update"

Read the information about the update and click "Next"

"Agree" to the license agreement

The software will start to download

Here the software is preparing the iPhone for the update

The update is being applied

The update is being verified

A firmware update is also being applied

Finally, a message will indicate that the update has been applied and that your iPhone is being restarted to complete the process.