An eclipse, by definition mean something is being blocked or covered. So a solar eclipse means the sun is blocked/covered and a lunar eclipse means the moon is blocked/covered. That is the first concept to understand. Next, you need to understand the relative positions of the 3 celestial objects involved, as seen from above the North Pole.
For a solar eclipse, the order is Sun-moon-Earth. It occurs during a new moon.
For a lunar eclipse, the order is Sun-Earth-moon. It occurs during a full moon.
However, eclipses do not occur each time there is a new or full moon because the moon's orbit is inclined by about 50 so all 3 celestial objects must be perfectly aligned to have a total eclipse.