The conformal coated (epoxy) dipped capacitors are usually (always?) film, either mylar (polyester, pop bottles!) or polypropylene, among a few other plastics used. Add some metal, either as foil or metallization, and you've got a capacitor. Well, add some leads and you do.
For low voltage ratings, the film gets very thin indeed. The cross-section may look gray, because the layers are so thin. It should be easy to crack open a higher voltage rated cap (say, 630VDC, 0.1uF or thereabouts) and unwravel it. You should find two long pieces of film, coated on one or both sides with metal or sandwiched with foil.
A ceramic capacitor is flat and has metallization on both sides. Film isn't a real great capacitor, as big capacitance goes, so they have to wrap up many square feet of plastic; a ceramic capacitor, however, has high density, so they get away with a small disk of this special stuff, metallized on opposite sides. Try to break off the brownish coating on one to see the construction.
Electrolytics are similar to film caps, except they use a gooey electrolyte absorbed onto, I think a special paper is used, and aluminum foil for the positive electrode. The chemistry is such that, when a positive voltage is applied, a layer of sapphire (aluminum oxide) grows on the surface of the aluminum. Aluminum oxide is a great insulator, so not much thickness is needed; as a result, capacitance can be pretty chunky, even considering the bulk of remaining foil and pesky electrolyte.
You can take electrolytics apart as well as any other, but I'd recommend wearing gloves... you don't know what they put in that goop!