Use your command line and navigate to the root folder of your project and enter

$ composer init

After that you'll get some questions ask in order to generate composers's configuration file `composer.json``

Package name (<vendor>/<name>): vendor/name
Description []: // leave empty
Author: Roland Loesslein <info@weaintplastic.com>
Minimum Stability []: // leave empty if not specified
License []: // leave empty if not specified
Would you like to define your dependencies (require) interactively [yes]? no
Would you like to define your dev dependencies (require-dev) interactively [yes]? no
Do you confirm generation [yes]? yes

To specify a directory where the composer libraries are saved to, please open up your composer.jsonand add the following line. I just tend to rename the default vendor-dir vendor to composer_vendor to follow the naming scheme that is used by Bower and NPM.

"config": {
    "vendor-dir": "composer_vendor"
}

You are now ready to install your third party libraries, frameworks and such using composer. Therefore you use your command line and the command composer require

$ composer require erusev/parsedown:~1.0

The installed packages are saved in your projects root folder named composer_vendor. While your frontend dependencies are usually not needed during runtimem but compiled for shipping, your composer dependencies are most likely used during runtime. Make sure to NOT exclude your composer_vendor folder from being tracked by git.

Make sure you don't commit and push your dependencies source files to the repository but exclude them using .gitignore when setting up your collaborative project