There are lots of ways to transfer files over the network. The easiest, in my opinion, is to use TCP/IP and set up a network share or mapped drive between the two machines and then transfer the file by using copy. Of course, there are lots of situations where setting up a network share isn't apropriate.
If network share isn't an option, and you want to use serial, you should probably use a protocol such as Xmodem, Ymodem or Zmodem to transfer the file. LabVIEW doesn't have direct support for these protocols, although I know someone sells (or at least used to sell, I couldn't find it with a quick search) a modem toolkit for LabVIEW with these protocols implemented. There are also ActiveX servers that implement these protocols that you could download or purchase and then access from LabVIEW.
If you want to go the TCP/IP route, an FTP server would be an easy option. You'd need to run an FTP server on the target machine, but then you could just use the LabVIEW FTP VIs or call an FTP terminal through command line or ActiveX.
Of course, you could implement your own file transfer protocol using VISA, datasocket or the TCP/IP VIs, but this last option is quite a bit of work to solve a problem when there are plenty of programs out there to solve it for you. Re-inventing the wheel if you will. While it's not all that difficult to read in a file, transfer it using one of the communication APIs, and then write it back to a file on your client machine, you'll either have to implement, or go without, a lot of the features and safeguards, like error checking, which are built into other file transfer protocols. Also, remember that you'll have to have a LabVIEW application running on each end, so you'll have to implement both halves of the solution (as opposed to options like FTP or the network share, where you only have to run a VI on one computer).
Hope that helps,
Ryan K.
