When you connect your iPhone to the computer running iTunes, it should begin the sync process automatically. If your phone isn't syncing with iTunes, it might simply mean that you have no new items to sync or that there's a problem with either the hardware or the software on your computer or iPhone.
Go to "Help > Check for Updates" (or "iTunes > Check for Updates" on a Mac) to make sure that you're using the most recent edition of iTunes. Make sure that you have the most recent update for the iOS system. If your iPhone refuses to update, you can back up your phone and do a full restore. Because each update adds something to the functionality of the program or the operating system, using an outdated version of the software or an outdated version of iOS can cause issues with syncing your data.
Sync Not Set Up
Your iPhone may not be syncing properly if you don't have syncing set up in your current edition of iTunes. Connect your iPhone to your computer and select it from under "Devices" to change your iPhone settings to set up the sync options. After you've gone through the process of setting iTunes to sync with your device, click the "Apply" button in the lower-right corner of the screen to start the sync.
Check the cord connecting your iPhone to your computer for any damage, including to the metal and pins on the ends. The iPhone only supports syncing data over USB cables. If you happen to be using an old iPod FireWire cable, the only thing you will be able to do is charge your iPhone. Test out different USB ports on the computer to see whether the data problem is just with one USB port.
Issues With Multiple Computers
You cannot sync your iPhone with multiple computers -- continuing to switch between computers for syncing your iPhone can cause issues with corrupt data or missing files. If you need to go back and forth frequently between computers, consider using a service such as MobileMe or Microsoft Exchange.