I have upgraded so many laptop HDDs, I forget the count. As has been stated, cloning is the solution. The key to good cloning is to get the software onto a bootable CDR. That normally requires installation of (eg.) Acronis True Image on some computer. Then create the media.
Put the new drive into an external powered case and connect it to your laptop via USB, Firewire or eSATA. Then boot the laptop using the Acronis media, and do a manual cloning operation with proportional mode - choose the source drive and the target drive. Complete the operation and then simply power down and swap the HDDs. The new, bigger HDD should boot right up if you did it right.
Another way is to use a larger external drive - clone to it, then replace the old laptop HDD with the new drive, boot with the CDR, and clone from the external to the new drive in the laptop.
Some laptops make it easy by being able to install two HDDs. Cloning is then direct and much faster. That sometimes removes the CD/DVD drive, and you have to create your bootable media on a USB flash device. That works equally well. I've done all of them.