"only that you transfer your documents to where Word expects them to be, and the default location is C:\Users\ your name \Documents\ "
Documents can be in other places, they don't have to be in that default location, it depends on how you organise your files. So you don't have to work out where that default folder is and copy the files there, the files will work wherever they are.
However you might want them there, if that's how you organise things, but that's your choice, you won't break anything by doing something else.
"I wouldn't advise simply transferring all of the C: and D: drives because you might end up with conflicts."
If you copy everything on the old C: drive to the new C: drive in exactly the same place then you will have trouble. However if you make a folder on C: called "The Old Computer" and then into that make two other folders called "C" and "D" then you can copy everything from the old C: drive to C:\The Old Computer\C and everything from the old D: drive to D:\The Old Computer\D without causing any conflicts or problems.
However what you won't want to do is to run any programs from those folders, that could very easily cause trouble. But doing this is a great and very easy way to make sure that you get everything off of the old computer and onto the new one and you can then hunt through it at your leisure to make sure you find everything.
As to how to do the copy....
"Will a pen drive be big enough to do this?"
Unless you have a very big USB stick (which is I guess what you mean?) and a very tiny old computer this is unlikely to work.
What you ideally need is an external USB disk drive to copy the files over with. That makes the process a doodle and you will want to be backing up your stuff somewhere as well as the computer anyway, so once you've done the transfer use it as a back up device. Never have the files only on your laptop, one day it will break and everything will be lost.