It's obvious that if you make the plates bigger, you'll be able to store more charge (just as if you make a closet bigger you can stuff more things inside it). So increasing the area of the plates also increases the capacitance. Less obviously, if we reduce the distance between the plates, that also increases the capacitance. That's because the shorter the distance between the plates, the more effect the plates have on one another. The second plate, being closer, reduces the potential of the first plate even more, and that increases the capacitance.
Chat: Different materials make better or worse dielectrics according to how well they insulate the space between a capacitor's plates and reduce the electric field between them. A measurement called the relative permitivty tells us how good a dielectric something will make. A vacuum is the worst dielectric and is given a relative permotivity of other dielectrics are measured relative(by comparing them) to a vacuum.Air is roughly the same.Paper is about 3 times better.Alcohol and water, which have polar molecules, make particularly good dielectrics.