As a PHP developer I find myself working with Composer a lot. In the past it was on personal projects and such so I didn't have much problems with it, but now with Laravel 4 it's on project that require deploying and I'm in kind of a struggle to adapt my workflow.
All my projects are git repositories, thus per convention and because it's still quite buggy, like most developers I put the
The best way is to run
composer install on the server after updating to the latest code. You should also make sure you commit your composer.lock file, which the server will then use to install (you should not run
composer update on the server).