My laptop is sony Vaio VGN-NR21E. The operating program is Windows Vista. I want to extend my laptop’s memory. I want to know – what is the maximum volume that I can install in my laptop?
you can use crucial scanner to find out compatible RAM and size
As Oron explained hard drive and RAM are two different things.
Vista Drive Capacity Limitations
Windows Vista 64-bit: GPT has a maximum disc and raw partition size of 18 exabytes,
Windows Vista 32-bit: MBR has a maximum partition size of 2 terabytes
Before answering, I'd just like to point out that the hard drive does not "extend the laptop's memory". It is storage space, which is technically a type of memory, but not what we normally call "memory". Your model of laptop can take a maximum of 2GB RAM ("real" memory), which is not an awful lot, so you should consider carefully whether it's worth the price and effort of replacing the hard disc.
Now with that out of the way, I had a quick look on the internet. I can't see any specific references to 1TB drives on your model, but there are companies selling 500GB and 750GB drives for it, so 1TB should work just fine. Just make sure to check the thickness of your existing hard drive and get one which is no thicker.