Before you read this post, I assume you have read getting started with a vNext project on a Mac.
ASP.Net vNext has been designed to be cloud ready. So, regardless of whether you are on Mac/linux/PC or using sublime or Visual Studio 2015 deploying a website with Github is going to be the same workflow.
Deploying ASP.Net vNext Project using GitHub
The first thing we want to do is hook-up your vNext Project from Github to Azure using Kudu (if you don’t have repository fork mine). This allows for continuous deployment from your Github repo to Azure. Kudu is the engine that can run within and outside of azure that allows for git/hg deployments, WebJobs, and various other features in Azure Web Sites. Kudu does this by generating deployment scripts under the hood and, deploy a website when pushing changes to a Github repo.