Well there are a number of ways to do this depending on the features on both computers:
1) If the Windows ME PC has a writable CD or DVD drive they could copy all the data to CD or DVD, then take it to the Vista laptop and copy all the data off the disk onto the laptop.
2) If the Windows ME PC has a USB port they could buy a USB memory stick, copy all the data onto the memory stick, then take the memory stick to the Vista laptop and copy it onto the laptop disk.
3) This may be too technical for them, but there are ways of connecting two computers together with a network (ethernet) cable and copy the files from ME to Vista like that.
4) This may also be too technical, but if they have broadband and a router they could connect both computers to the router and then "share" disks between them and copy data from the ME computer to the Vista laptop.
5) Some websites allow you upload data and store it there. They could upload the ME data to the website, then logon to the website with Vista and download it from the website (never done this but I guess it could be done).
They are the main ones I can think of at the moment.