what is the best way to manage 30 web server application

I have 30 web server running the same web application, what is the best way to manage this, if having file changes in this application.

For now, if having changes/bug in the web, I will manually upload the file one by one to each server using FileZilla. I things this is not right to do.

I have a look on github and bitbucket on versioning control but not understand how this think can apply on my situation.

Hope, anybody can give the idea on handling this situation... Thank you