Is there some kind of an easy way to send files from my desktop to my laptop through LAN?
I'm completely clueless about network stuff.
Make a folder viewable on the network (sharing options) and then simply browse the network computers:
On file/folder:
Properties -> Sharing -> Share... -> Add (Everyone or specific, like Homegroup)
On the new PC:
Start Menu -> Network -> [PC with the files] -> [Folder with files] -> Take files.