For example, I have made two commits to the github so far, one was the starting point, and the other was adding the movement phase. You can see the commit history of a branch by clicking this button which gives you a file by file breakdown of the exact changes made.

Im still learning how to use github, but essentially the flow is that anyone who wants to contribute can download the project (known as cloneing the repo), make some changes, then push them back to the github. Then authors can pull those changes to their local copies. It's a very distributed model that helps everyone be working on the latest version. It also allows merging two versions together easily so long as you didn't edit the same files at the same time. With big projects and lots of contributors its common for one or two people to be responsible for merging and making sure you don't break things, but thats more relevant for company software so they don't break their websites and such.

Latex really isn't that scary if you don't open the .cls template file. Which is kinda the paradigm of Latex to begin with, authors just write text, editors format templates. If you open any of the .tex files (which can be opened by any plain text editor like notepad, sublime text, or notepad++) you will see it's all very clean and easy to understand (and replicate) if you have a starting example.