Syncing iPhone Between Mac and Windows computers iTunes 10

To sync your iPhone between a Mac and a Windows computer, there are 2 files that need to be copied from your primary computer to the other.

In Windows in Libraries\Music\iTunes	On the Mac in Users\<username>\Music\iTunes
iTunes Library.itl	iTunes Library
iTunes Music Library.xml	iTunes Music Library.xml

Notice that iTunes Library.itl is a different name on the Mac.

Here are the steps in detail:
Step 1) Exit iTunes on both computers
Step 2) Locate the 2 files on your primary computer (Where you normally sync your iPhone with iTunes)
Step 3) Copy the 2 files to a USB drive
Step 4) Rename "iTunes Library" to "iTunes Library.itl" or vice versa on the USB drive
Step 5) Locate the 2 files on your second computer and make a backup copy
Step 6) Copy the 2 files from the USB drive to the second computer
Step 7) Plug your iPhone into the second computer, start iTunes and sync.  This step can take quite a while depending on how much data is on the iPhone.  Mine took about 10 minutes.
Step 8) (optional) Authorize iTunes