If you insist on putting a new hard drive inside your computer, this explains how to do it:
http://uk.pcmag.com/storage-devices-reviews/14364/feature/how-to-clone-a-hard-drive
If you're going to follow the cloning route then, as suggested in that article, Acronis software is probably your best option. (If you were to ever be suspected of something naughty by the police or security services, that's what they'd use to clone your hard drive, so that they could then work with the clone and leave the 'evidence' untampered with. It's definitely the 'benchmark' software for the job). However it will cost you about 24 quid:
http://www.acronis.com/en-gb/personal/pc-backup/
However, as Z-M suggests, an external drive would be a far simpler (and probably less costly) solution anyway.