Transferring files between computers using Java can be achieved through various methods, depending on whether the connection is over a local area network (LAN) or the internet. For LAN transfers, using `ObjectInputStream` and `ObjectOutputStream` is suggested, but it is emphasized that actual networking classes like `Socket` and `ServerSocket` are necessary for file transfers across networks. A simple protocol is recommended for communication between the two computers, particularly to handle file naming and transfer commands. While some participants mention alternatives like Remote Method Invocation (RMI) and File Transfer Protocol (FTP), it is noted that RMI is not suitable for file transfers and that implementing FTP may be overly complex for simpler needs. For internet transfers, establishing a basic protocol without the complexities of FTP is advised. Additionally, using mounted network drives can simplify file writing on a LAN. Overall, the discussion highlights the importance of understanding networking fundamentals in Java for effective file transfer implementation.