To change file permissions, use Properties function (File menu).

Mode 666 means that everyone has right to read and write the files. Mode 777 means that in addition to reading/writting, everyone can execute the files and enter the directories. You probably get the better idea, when you try to switch the checkboxes on Properties dialog and see how octal number representing the permissions changes. The link above points to screenshot showing mode 750.

I have been trying to upload a text-based message board, and it calls for me to upload them in the chmod 666, and some files in chmod 777. I have no idea what this is, but is this even possible to do with WinSCP?

Thanks