Capacitors are made to store charge - like a tank for water is made to store water. They can be filled with electrical charge and the voltage rises accordingly. Double the charge and the voltage doubles, similar to a water tank where the height of water level doubles if the amount of the water in it is doubled. (And accordingly the pressure at the bottom also doubles).
Different sizes of capacitors can be visually imagined as differently sized tanks. A very thin tank will rapidly be filled to a certain level while a very tall tank has only a thin layer of water on its ground.
The unit determining the capacitance of a Capacitor is called Farad: A capacitor of one Farad has 1V when filled with 1 Coulomb of charge. A Capacitor of 0.1 Farad needs only 0.1 Coulomb to be filled to the same voltage level.
In practice a capacitor of one Farad is comparably large. Common capacitors have capacities in the range of nano-Farads (1 nF = 1/1000 000 000 th) up to several micro Farads (µF). So they are like very thin and tall flower vases where small amounts of water cause a strong rise of the water level.
Voltage rating: The voltage printed on a capacitor is an absolute maximum rating which can be used without harm to the capacitor. It should not be exceeded - otherwise the capacitor can be destroyed. It's generally a good idea to use capacitors of approx. 20% or more above the actual voltage planned to use as higher voltages may occur or the capacitor might be a "bad one" which doesn't stand the labeled voltage.
There are two basic types of capacitors which should be distinguished: The ones which have a polarity (usually marked on the component with a - or a + sign). All remaining capacitors don't care about polarity. The ones which have a polarity are easily destroyed when used in reversed polarity - apart from that there's no difference in their function as electronic part.
Early capacitors were made of 2 metal plates, arranged facing to each other. That's also where its symbol comes from - showing the 2 plates from the side. This is already a very simple capacitor (with a pretty low capacitance though).
Obviously metal plates don't care about polarity as they are almost identical and so can be interchanged without anyone noticing a difference. These plate capacitors were physically pretty large capacitors but their capacitance is pretty low. To save space and increase capacitance the 2 plates can be made of metal foil and the air can be replaced by an electrically insulating layer in between. To save even more space the foils can be rolled into a tube. (Insctruction to create your own capacitor of foil) This cylindric form of foil capacitors was very common for a long time -but nowadays foil capacitors are mainly rectangularly shaped blocks. There are still few current foil capacitors which are cylindrical - but most of today's cylindrical capacitors are of an other kind (the elctrolytic capacitor, see next section about polarized capacitors).
An other type of an unpolarized capacitor is the ceramic capacitor. Here the plates are insulated by ceramics instead of foil - increasing the capacity and maximum voltage rating. Images on wikipedia
Electrolytic capacitor: This kind of capacitor needs to be connected in the correct polarity or it will be destroyed. (There are spectacular videos on youtube of explosions occuring when connected to reversed polarity). They are basically cans of aluminium filled with an electrolytic fluid. The two plates are gone, but are replaced: one "plate" now is the electrolytic fluid, the other one is the can. Between the can and the fluid a thin isolating layer exists so they don't connect - like the foil in the foil capacitor. As the 2 "plates" are no more identical like the metal plates were in the foil capacitor the symbol also changes: one side is thicker or bent and no more similar to the other. However there are also symbols where only a + or - sign marks one side of the capacitor. Have a look at the wikipedia page for its symbols.
An other form of a polarized capacitor is the tantalum capacitor (image). They can easily be confused with ceramic capacitors which often come in a similar looking case. But their much larger capacitance can be used as a hint that it's not a ceramic capacitor:
Ceramic capacitors are in the range of pF to few nF - tantalum capacitors range from several approx. 100 nF to several µF.
Also as they should show signs of a polarity on them. If in doubt the capacity can be measured using a digital multimeter (if it has capacitance measurements) and this can be compared with values printed on the component - or with their colour coding.
Capacitance varies when different materials are inserted or removed between the 2 plates of a capacitor. For example the capacitance increases when air is replaced by a dielectric (like the plastic foil of the foil capacitor or other insulators).
In old radios variable capacitors with a rotary knob are found that look similar to a potentiometer. You can recognize plastic foils and thin metal plates which move when the knob is turned. (Example images on wikipedia)
Those are the cheapest kind of capacitors. Widely used in every day's electronics are values from 0.1 µF up to 100 µF. They are also small and pretty cheap to buy. Increasing capacitance will be more expensive and usually much larger. The same is for voltage. Typical capacitors are designed for maximum voltages of 25 V to 100 V. There's also a temperature given for the capacitors. The higher the better the quality of the capacitor.
Electrolytic capacitors aren't made for infinite lifetime. If you plan a circuit which stands usage for 100 years chose other capacitors instead. Not they also suffer from higher temperatures than labeled (their fluid will escape, rendering them useless).
Available up to several 100 of Volts.
Film capacitors are much more expensive for the same value of capacitance and voltage as an electrolytic one. Also a 1000µF type would be incredibly large. They are much mor durable than Electrolytic capacitors and theoretically can live forever. If they aren't sealed water can get between the foils and reduce capacitance or even cause current to flow where it shouldn't. (Modern Foil capacitors are fully sealed - you will see the foils if they aren't).
Available for voltages up to several 1000 of Volt.
Calculate lowpass filter (using a capacitor and a resistor, german):
Measure capacitance using Arduino: