For connecting VCR to computer you will need a video editing card or TV tuner. The cheapest device from this category are less than 50$, but to obtain better results it would be better not to skimp and buy a tuner with hardware encoding the stream to MPEG2.
When buying, make sure that the tuner or video card have a composite or component inputs (better yet S-Video).
Connect the video output connector of a VCR (only video signal) to the input connector on the tuner Board or video capture. You may need an adaptor, but the adaptor of this type easily purchased in any tent.
The audio cable from the VCR connect to the input of your sound card. This will require an RCA to minijack.
Install the video editing software, e.g. VirtualDub. Set up as a video input on your tuner (or charge editors), and as an audio signal to your soundcard. Set video encoding settings and save your movies in digital format.