There are many ways to move files between systems on a home lan. If all machines are linux, you can set one up as a FTP server, and run a FTP client from the machines you want to copy file to. FTP can send and receive files.
If you want to do more, like edit a file on a remote machine, and store the edit on the remote machine, then set up SSH, again this is a client to server thing. You can set all boxes up to be a server, then you can secure copy as well as get a secure remote konsole to do anything you want. SSH replaces telnet, telnet is not secure.
If you want to be able to treat remote files on another system as files on your own system, set up NFS on linux systems. This again is a clinet sever arrangement. So the box sharing the files is the server, and the box accessing the files is the client. All linux boxes can be set up as servers.
I would recommend you do not think about Samba, this is for sharing files and printers in a mixed network of linux and windows systems. Samba will work between linux systems, but it is much more difficult to set up than NFS.
There are tutorials under networking to set up these types of configurations; on this board. I followed the NFS tutorial, and had it working in about an hour. Samba will take much more time for someone new to linux.
So in summary, define your needs, pick the use you need, and install the appropriate servers and clients, and configure.
Hope this helps.