Even those who don't believe in the Force and aren't particularly attuned to its flow can call upon the Force without understanding exactly what they are doing. When a stroke of amazing luck occurs, or fate seems to be on your side and helps you accomplish a difficult objective, it could be the Force coming to your aid. When a Force-using individual calls on the Force, he or she knows exactly what's happening and gets a more impressive boost because of it.
The most prominent and well-known Force-users in the galaxy are the Jedi. But the Jedi are not the only ones who have learned to manipulate the Force. These others sometimes attribute their abilities to sources other than the Force, such as magic or gods, but they all are using the energy to manipulate the world around them.
Other Force-using traditions include the various dark side cults - including the Sith - obscure, isolated sects such as the Witches of Dathomir and the Sorcerers of Tund. Some know the Force for what it is but approach its use from a different direction than the Jedi. Others know the Force by a different name. Either way, it remains the mystic energy that binds the galaxy together and gives Force-users their powers.