There are 3 ways by which you can carbonate water. You can either mix the acid into the water by shaking it or you can wait for some time for the mixing to occur naturally or you can even allow some of the acid to evaporate after you have increased the level of carbonic acid in the water. If you have a Ritchie carbonator or any other similar machine then you could even mix carbonic acid to wine or any other beverage including water. This is not possible with a soda machine. However, in this process you will have to alternately carbonate and then wait for some time before carbonating again, and then repeat the process again. This process is certainly not suitable when you simply want a revitalizing drink immediately.   

 This video displays the method used to carbonate water into a soda bottle through a home made machine. The carbonic acid is put in the water and shaken to mix it once the pressurizing is done.

 Since carbonic acid in big CO2 bottles is not costly at all, this method is okay, but a better method is to simply over pressurize since this will eliminate any shaking or waiting.

 It is also better to refrigerate your water first to make it cold as carbonic acid dissolves quickly in cold water. Over-pressure techniques are also employed by all commercial soda making machines.

 The PET bottle that you choose should be very strong, since once you partially fill it with water then you will have to pressurize it just like the other sodas that you purchase in such PET bottles.

 Carbonic acid should then be added until the sound of the pressure valves releasing is heard, before releasing the button to equalize the pressure. You can adjust the level of carbonic acid as per your tastes and if you do want to increase the level of carbonic acid then simply repeat the above steps. Once you add flavor for carbonated water then you can also improve the taste of the water.

 This German video shows you the method of carbonating water while using the Sodastream machine and the carbonated water can be instantly ready for you to either drink it or even add flavors to it.

 Since the bottle has increased strength as compared to other bottles, this method is the best and the bottle too will last for a long time.