Ok. It sounds like you have Vee brakes. On these, as the cable enters the brake , the inner wire passes through a curved metal tube called a "noodle". Does this sound like your brakes. Proceed as follows. squeeze the 2 calliper levers together, and at the lower end of the noodle, disengage the cable inner wire from its slot . This will allow the calliper arms to move apart. Using an allen key, remove the bolt on one of the calliper pivot points. Gently pull the arm from its pivot about 2 mm. You will see a spring protruding from the arm and engaging in a hole in a small plate welded to the frame. Often there are 3 holes. Note which hole is used. Carefully remove the arm, and clean and grease the pivot. Now do the other side. There are often 2 ways to adjust spring tension. One is to move the spring end to a different hole . Some brakes have a screw on the outside of the arm near the pivot . Tighten to increase tension.
Also note that poor cable routing near the noodle can pull the brake onto one side of the wheel . Hope this helps.