If the old laptop isn't too old to still be in legacy archives, you likely can download a "service manual" from the manufacturer's website. That should give you sufficient instructions to get a hard drive out without major damage to the laptop.
You can get cases for 2.5" drives with USB translators built in, so that you could pop it into a case and use it as an external drive. If you can find a decent USB case, that's an easy way to transfer everything to the new computer.
If you don't want to put the drive back in the old computer, you could then just use it, in the USB case, as an external drive for overflow or backup.
Vista supposedly has an available accessory program for "transferring everything" using a USB or Firewire "zero modem cable." I've seen "rumors" that a similar utility and cable setup is available for WinXP but haven't looked for details.
USB cases are, as Richard says, easy to find, but many of them only accept IDE/EIDE drives. I've got a couple that will take either an IDE or SATA drive, to USB; but I've only seen a few of those in my local shops. Most of the dealers here haven't even heard of them - and the SATA-capable ones that I've seen are all for 3.5" drives.