Carbonation is the process of adding carbon dioxide to water and water-based products, including soda, beer, and mineral water.
H2O + CO2 -> H2CO3
In general, it requires very little carbon dioxide to carbonate a beverage - 4 grams at high pressure is enough to agitate a cold 2-liter bottle of liquid with ease. This is based on Le Chatelier's Principle, which dictates that decreasing heat favors the products of the reaction, and Henry's Law, which states that the concentration of a solution is directly related to its partial pressure.
In general, purchasing a tank for CO2 storage in one's home is fairly affordable, and $20 will get you 20 pounds of dry ice - enough for nearly 600 gallons of liquids! Alternatively, proponents of homebrewing offer carbonation drops, which greatly reduce the amount of effort and chemical guesswork involved in creating beverages on your own.