Once you restart your computer (if you had to restart it), open iTunes again. You'll have to review and accept the iTunes Software License Agreement before the new version will launch.
When you have iTunes open, connect your iPhone to your computer using its USB cable. (You may see your computer automatically installing the necessary drivers; if so, let this run.)
Once all the necessary drivers are installed, iTunes will recognize your iPhone. The phone's name (which you gave it when you activated it) will appear under the "Devices" heading in the menu that runs on the left side of the iTunes screen.
iTunes may begin backing up and syncing your iPhone automatically, depending on whether or not you've set it to sync automatically. If you haven't set up automatic syncing, you can do it manually.