Downloading and Installing the iTunes 10.0.1 Update
You will likely be prompted for the iTunes 10.0.1 update when you first engage iTunes with something, such as plugging in and syncing your iPhone. You can just initiate the iTunes 10.0.1 update right then, or you can do it manually. When iTunes is open just go and select the iTunes prompt in the upper task bar, and then select Check for Updates from the list. A prompt will then come up asking if you want to download and install the iTunes 10.0.1 update.
This will begin the Software Update process and it will start by checking for and identifying the exact software update that you want. This may actually show multiple software updates that are not just the iTunes 10.0.1 update if you have other updates waiting on your Mac, and you can choose to keep them all checked or to jus t check your iTunes update.
Once you have iTunes checked and are ready to go hit the Install button, which will say 'Install 1 Item' if you are just installing the iTunes 10.0.1 update. You will be asked to log in with your administration password if you have that set, and once you do the iTunes download will begin. You can watch this as it happens in the progress bar and it will tell you the percentage at a time.
At a certain point in this process you will be prompted to close out iTunes to complete the iTunes 10.0.1 update installation. When it has finished it will let you know and then re-open iTunes, updating the library and initiating a sync of your iPhone if it is plugged in.