We are working on a team of developers, So we want to add a local git server between us. We are developing on Appcelerator, my Question is how to access the local repository from other apple machines using local network?
Give a try to Gitlab or something similar. They have unlimited private users / repos / groups even for free. Also, you can host it by your own in cloud or dedicated server.
Anyway, I suggest you to read this chapter in 'Pro Git' book to discover all the possibilities. For example, it describes how you can set up your repo with HTTP(S) using Apache.
And, you definitely need to share git repo from user to user, than just share the directory as usual in Mac (I do not know how to do it on Mac, but on Linux you can use Samba, on Windows it is just regular sharing) and then access it like \\windows-machine\\shared\repo\.git (that's how Windows shares looks like in network).