The 160Gb drive may have software to clone the the 20Gb drive. You would just set the 160 up as a slave drive, use the software. Shut down the computer and take out the 20Gb, if you want to. Then set the jumpers on the 160Gb to master and away you go.
If the hard drive has no software, just go to the manufacturers website and download it.
What make and model is the 160Gb.
Are you sure your computer will recognise a large hard drive, it's just that with your main drive being just 20Gb, your bios may have a limitation to what size of hard drive it can take.