Using the damper pedal effectively is an important technique for pianists to master.
Another name for this pedal (the right pedal on a grand or upright) is the sustain pedal, because it sustains the sound by suspending the contact of the hammer to the strings.
The first step to learning how to use the pedal is to press it down the pedal at the proper moment. This happens right after you press down the piano key. Practice and master this technique first.
The next technique is to practice changing notes or chords with the fingers and quickly (but gracefully) lifting and pressing down the pedal again.
The guiding principle is that we lift the pedal whenever we move to a new harmony. This prevents notes from clashing with each other, and it controls the "wash" of sounds that we would create if we kept the sustain pedal down longer.