Here are several ways you can make carbonated water without using a soda maker machine. The reason why I recommend buying the machine is for the convenience, especially if you are a frequent drinker of carbonated water. If you only have occasional use for soda water, then you can use one of the methods here to make carbonated water at home.
Method: Use Fizz Giz caps and co2 tank
This is real easy to do. Get one of these Fizz Giz caps that allows you to pump co2 into the water, like how the image above does it. Simply hold the bottle upside down and use the co2 pump through the caps. You will see bubbles forming in the water if it is done correctly.