You may install Composer locally, as part of your project, or globally as a system wide executable.
To install, run these commands in your terminal.
php -r "copy('https://getcomposer.org/installer', 'composer-setup.php');"
# to check the validity of the downloaded installer, check here against the SHA-384:
# https://composer.github.io/pubkeys.html
php composer-setup.php
php -r "unlink('composer-setup.php');"
This will download composer.phar (a PHP Archive file) to the current directory. Now you can run php composer.phar to use Composer, e.g.
php composer.phar install
To use Composer globally, place the composer.phar file to a directory that is part of your PATH
mv composer.phar /usr/local/bin/composer
Now you can use composer anywhere instead of php composer.phar, e.g.
composer install