The quickest way is to buy a USB portable drive then do as follows:
Connect via the USB
Use a disk-imaging program such as Ghost, DriveBackup or Acronis to image your existing drive to the USB one.
Remove the USB drive from its container and swap it for the drive in your laptop.
Reboot.
You now have a larger drive in your laptop, plus an external one for backups, archives etc, and the only software you've had to install is the disk-imaging stuff.
I've done this a number of times and (excluding the time to create the image, when you can be down the pub) it takes about 12 minutes.