Ethel's answer is excellent. However, it occurs to me that you might want to edit the transferred video data, rather than just copy it. If so, transferring it to your PC might still be worthwhile.
The output from a VCR is in analogue format, whereas your PC only handles digital data. So you'll need a suitable gizmo to convert the analogue signal to a digital one.
You could buy an analogue TV card for your PC. Many (but not all) of these have sockets for accepting an external video feed. (With the switchover to digital TV, many dealers are now selling-off analogue TV cards very cheaply). However, that means opening up your PC to install the card. (It's a very simple job but not everyone is happy fiddling about inside their PC).
An alternative way of converting the analogue signal to a digital one, and getting it into your PC (without having to open the casing), is to use a special gizmo which plugs into a spare USB socket. The only one I know of (and which I can also recommend from having used it myself) is this:
http://www.lambda-tek.com/componentshop/index. pl?origin=gbase20.3&prodID=494478
Whether you use a TV card or the USB-Live device, you'll need a 'Scart-to-AV' cable to connect between your VCR and your chosen device. These cables (which are also known as 'Scart-to-phono' or 'Scart to composite video') vary widely in price. When I last bought one, the cheapest Curry's could offer cost �19.99. I went to Tesco instead, and paid �1.97. So it's worth shopping around!
Lastly, you'll need some suitable software for recording and editing your videos, but the USB-Live device (and analogue TV cards) come supplied with appropriate software anyway.
Chris