Which of the following components should be added to a capacitor to increase the capacitance?
Why Capacitors in parallel add directly: C_total = C1 + C2 + ... Putting another capacitor across the first is electrically the same as enlarging the plate area, so the total charge stored per volt goes up. This is the opposite of resistors, which add in series.
Watch out Adding a capacitor in series lowers the total (1/C_total = 1/C1 + 1/C2), always giving less than the smallest capacitor. Inductors do not change capacitance at all; they form a resonant circuit with it.
Capacitors behave backwards from resistors: parallel adds, series divides. More plate area in parallel means more C.