How to carbonate a drink?
How to do it - practical advice  

You need a machine for carbonation. There are different brands. You buy cartridges with gas for them, put the bottle with the drink in the machine with the loaded cartridge, and press a button a few times. The drink is then carbonated. 

I there are also combined whippers/carbonators which can alternatively take a nitrous oxide cartridge to make foams. This is too complicated and unnecessary if all you need are carbonated drinks. If you are like most people out there, you want the simple system which just carbonates. 

Update: Some more words on what forms of carbonation are available 

Carbonation is a process in which you get CO2 bubbles dissolved in a liquid. The gas doesn't stay dissolved for a long time, it starts "seeping out" of the liquid, forming tiny bubbles, which rise through the liquid, giving a prickly feeling on your tongue when they reach it. 

You can get the gas into the liquid by three general classes of
   methods: add an organism which produces CO2 (biological method), add
   a compound which reacts to produce CO2 (chemical method), or add the
   gas directly (physical method).


Adding yeast is a biological method. Yeast metabolizes parts of
the drink, and releases CO2 as a byproduct. This needs time for the
yeast to live enough to produce enough waste gases, and it indeed
changes the taste, as the yeast eats up some nutrients itself, and
releases other byproducts beside CO2. These disadvantages are common
to all biological methods, no matter which kind of microorganism you
choose. 

You could also use a chemical method. It also changes the taste,
as compounds within the drink are used up in chemical reactions, and
there are also products beside the CO2, which have a taste of their
own. A further problem is that you can't get much gas produced that
way, and what you produce dissipates very quickly. So, it is not
advisable to carbonate drinks using chemical methods. 

The third way is the physical method. You don't produce CO2, but
add existing CO2 into the drink. Normally, if you just bring a drink
and CO2 gas together, the gas won't dissolve. What you need to make
this work is to release CO2 into the liquid under pressure. The
instrument which does this is a soda-making machine; it gets a
cartridge of CO2 under pressure. When you push the button, the
cartridge is opened, and the pressurized gas escapes from the
cartridge into the drink, where it gets dissolved. This is the
easiest method of the three, and has no disadvantages beyond the
investment in a machine and cartridges. There are inexpensive
machines for home use, so it is what I advise you to use.


Manufacturers sometimes combine machines which can expel CO2 from cartridges with machines which can expel NO from cartridges. Expelling NO is used for whipping foams, e.g. creating whipped cream. The whipped cream spray bottles in the supermarket are a simplified version of such machines, which cannot be reloaded. 

While the construction of CO2 expelling machines and NO expelling machines is similar enough that it makes sense to combine them in a single body, the use cases for CO2 use and NO use are very different. If you only want to carbonate, a CO2 machine is sufficient.