That depends. I don't commit my vendor folder so I have to run composer on the server.
Generally the vendor folder isn't included in git, once you have cloned this on your live server, run composer install and then create any needed config files that aren't in your repo.
You can also setup your staging/production server as a remote repo and use a post-receive hook to checkout and deploy the files into the proper serving directory. As a secondary task I normally have my post-receive hook delete the storage cache and run composer to install any possible new libraries that might have been added.
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