I mostly use Chrome or Safari to navigate and would like to enable touchpad scrolling.
I assume you are using Windows (even though you didn't say so) since you've tagged the questions with that OS. The exact method to check or enable this will depend on the exact model you have - but the principles are the same for all.
First - how do you know it does NOT work now? Typically you stroke the far-right edge of the touchpad for vertical scrolling and the bottom edge for horizontal. Try it - you may find it already works.
Some touch pads support two-finger scrolling - for that you use two fingers slightly separated anywhere on the touchpad and stroke in the direction you want to scroll.
Is it working in some programs and not others? From your question, I gather it's not working at all - correct?
If it is not working anywhere (and you've tried my suggestions above), in Control Panel, you need to find the dialogue that controls the touch pad. Usually this is a tab on the Mouse Properties (you can search for it in Control Panel - or click on Hardware and Sound and then on Mouse). Find the section for the touchpad and then you should have options to enable the touchpad, enable scrolling, set the scrolling region, etc. Once you find it, it's pretty self-evident how to set it.
If you verify that the settings are all correct and it still doesn't work - you may have a hardware fault.
Hope that helps,
In Control Panel/Mouse I was able to activate scrolling under multitouch functions.
I just found the solution for enabling scroll for VAIO.
The touchpad driver will be updated. You will need to restart your PC.
Scrolling should start working.