A low level of brake fluid can cause a spongy, soft or springy brake pedal as well. If the brake fluid is low, that can be very simply remedied by adding some brake fluid to bring it up to the correct level. If the problem is a low quality brake fluid, you will need to drain the brake fluid and replace it with a good brake fluid.
Any time the hydraulic system is disturbed, whether replacing brake hoses, adjusting hoses or faulty hoses, the system must be bled. One indicator that the system needs to be bled is a spongy or soft brake pedal. You will typically need to have a second person available when bleeding the brake hoses. This person only needs to be available to pump the brakes from inside the car several times; they need not have any special mechanical knowledge.
With the engine off, pump the brakes multiple times, 10 or so times to remove any remaining vacuum in the booster. Safely secure the front of the car appropriately on blocks with the back blocked off.
Attach a length of hose to one of the bleed valve and insert the other end into a jar with clean brake fluid. Open the bleed valve ¾ of a turn and have the second person steadily apply pressure on the brake pedal. When the brake pedal reaches the floor, return the bleed valve to its original position, the second person should then release his foot from the brake pedal - allowing it to return to normal position. Continue to repeat this process until no air bubbles come from the length of hose. Repeat on other wheels as necessary.
Be advised that a professional on the following vehicles must bleed the brakes: Chrysler Corporation cars from 1969 to present, 1969 Lincolns and 1970 to 1972 Fords, Lincolns and Mercurys.
To turn off the brake warning light on most modern model vehicles, simply turn off the vehicle, turn the key to the ignition position then pump the brake once. Older model cars may require replacing the warning light switch. To determine if you will need to replace the switch on your vehicle, ask your auto parts dealer.