First, you need some software.
Putty for remote access.
You want the 64 bit MSI install file.
WinSCP for file transfers.
To transfer files, you will launch WinSCP. You will specify a machine and login credentials as seen in the picture below:
Once you are connected, you will have a two pane window---your local machine on the left and the remote machine on the right. You will click on the files and select upload or download.
Once you have a file on the remote machine, you can use putty to remotely work. Once you have connected, just use the normal Unix commands (gcc, make, etc) to compile code. To run code, just type the name, although you will have to use ./ before it to specify the current directoy.