After you get the assignment to work. You will most likely need to turn it in so that it works on the Linux machine. To do this, you would use SFTP (or other secure File Transfer Protocol program) to transfer your files from your home to the Linux lab. Then you would SSH (remote login) to your account and compile and test the program one more time. If there are any problems, they should be fixed. Once the code works on the Linux machine, you can go ahead and submit the program depending on the regular instructions.
Note if you are testing a graphical program, like for graphics class, you won't be able to use standard SSH alone to test it. You will need something like an X connection to get it to work. See the next example. If you don't want to use CygWin (Windows users), then you may want to do the final test in the lab itself.
For this, I recommend installing something like CygWin which provides you with a unix-like operating system on top of Windows. CygWin provides X and SSH so you can run X and then SSH with X access. But be warned, CygWin is not easy to use at least not at first.