Identify and Download
The neat thing about drivers is that, no matter whether you need a keyboard driver, a mouse driver, or a webcam driver (or any other kind), generally speaking the manufacturer of your laptop will have them ready and available for free right on their website. Because of this, the first thing you'll need to do is head over to Sony's website.
Once you get to the main page, move your mouse over the "Service and Support" section, click on "Electronics", and then select "Drivers and Software". This will bring you to a brand new page where you will see the "eSupport" label on top of the whole page. If you don't see this, you may have done something wrong, so try again.
Next, you'll need to input your device type (in most cases, you're probably using a "Personal Computer: Laptop," or the similar option) in order to get to the drivers page, but once you do this the website should identify your specific Vaio model without any input needed from you. Once this finishes, you'll be on the page with your list of drivers and things, so all you have to do is click the "Keyboards" section and download/run the client. After it finishes, restart your laptop and you're done.