Turn based multiplayer help

Hey guys, I’m asking a ton of questions so sorry about that… I’m just new and want to jump in and learn.

So I’ve been scavenging the net for the past week or so trying to find an answer to this question myself but havent quite got there. I’ve found a few ‘tutorials’ but they dont answer my question, they handle the set up for a room or something but dont explain how to handle the turns or game actions.

Anyways, I’m working on a turn based multiplayer game as a little project and need some advice on the basics.

First off, i’ve run into a few places which offer the service, app42, photon, moai among others and i need to decided on one, so far I dont understand any advantage or disadvantage to any of them. I’m just looking for something thats cheap and preferably free as this is my first project and is a for fun thing not an investment.

Secondly I’m a little confused as to how to integrate the game actions into the ‘online’ bit of it.

i.e how do i make both players see the same screen? or how do i make each players turn?

sorry if these are bad questions to ask im just a little lost after a week or so of searching.

basically i’m wanting to know how to start a ‘room’ or a game between two players, and how to handle the two player’s turns. 

Any help would be appreciated, but please dont just point me to tutorials, i’ve looked through this site and others for the past week trying to work them out.