Simple Server Based Game - C++

Background: I am doing a project for my programming course. As part of the project, I have opted to attempt to create a simple server/client program to run our game in. Our game is a simple 2D game which takes at most 4 commands from the player and there will be no more than two players at a time playing. * I am not asking for code! * I found Beej's guide and a few other tutorials for creating a server and client program and I feel they will be fine for what I am trying to do.

Questions: i) What is the concept (in simplest terms, please) for how a server based game works? ii) I am programming in a Windows environment; will this create any issues with implementing my program in a Linux-based environment (particularly regarding Winsock)?

Nuances: i) I am programming in C++. ii) I would prefer not to use any non-native libraries (Boost.Asio, etc) iii) I have used Google and searched is StackExchange for help, but I was unable to find much in regard to my specific questions. If you know where I can find suitable answers to my question, please point me there.

Thank you for your help.