If you do not have a USB powered portable Hard Drive then I suggest that you buy one.
Plug it into your old Laptop and using Windows Explorer drag and drop the My Documents folder from your old Laptop to the portable Hard Drive.
Repeat for any other folders that you have stored on the Laptop that are not in the My Documents folder.
Reverse the procedure with your new Laptop.
It is always great computer management to have at least two and ideally three copies of all documents with each being stored on separate Hard Drives.
I use Western Digital Elements 2Tb Hard Drives that currently cost c£65, but other makes are fine. I prefer these because they are powered via the USB socket other can require their own power supply.
Finally, on my PC I regularly make an exact copy of the content on the My Documents folder on to my USB Hard Drives using a free program called Free File Sync, it is very easy to use