Symfony has a pretty solid security system, you should implement your login system it's way. You can find information on how to integrate the traditional login system with a database in the Cookbook.
If you are authenticating your users this way, fetching the current user becomes easy:
$user = $this->get('security.context')->getToken()->getUser();
Or, if you're inside a controller action:
$user = $this->getUser();
There's also the FOSUserBundle, which gives you some great tools to handle common user management at your system.