Deployment from Git to production server for beginners

So I’ve been using EE for several years, but as a casual freelancer I had been stuck in the newbie method of simply using an SFTP connection with the production server to my local machine.

However, I now want to expand into a more professional workflow by using BitBucket to manage my master and staging branches.

Where I’m drawing a blank is how to deploy the staging and master branches to my remote staging server and the clients’ production servers respectively.