How can I get rid of garlic breath?
Before answering directly to the quesiotn, a little forword is needed:

The garlic contains allicina (alliisina , glucoside solforato), an enzyme (alliinasi), vitamine A, B1, B2, C and niacina (another vitamin in B complex).

What happens is that there is a serie of chemical reactions when you chew the garlic, with the result of creating allile disolphour, which is what have the typical garlic smell.

The latter substance is very volatile and easily get in solution in liquid and gases.

So.... (this is the interesting part) when you ingest it, the propagate almost everywhere in your body. That's why you can smell it thorugh the organs which eliminate this substance, that is to say lungs, kidney, skin.
Hence, in conclusion, when you eat garlic, it is not only a problem of your breath, but your whole body smells of garlic (in fact if you make sport and you sweat, you'll see you smell of garlic).

This said, here are some remedies for the breath:


Chew sage leaves or prasley
Chew cofee grains
Drink a liquorice or mint decoction
Chew liquorice stick 
Chew anice grains
Eat slowly a honey spoon
Eat slowly an apple
Drink slowly a grappa
Drink some milk or some yougurt spoon
Chew slowly some lemon slices 
Drink some sodium bicarbonate.
last, use mouthwash prepared with cloramine solution at 1%; the clorite will get in contact with your body tissues, mitigating the garlic essential oil effect.


In any case, after a while (maybe hours) the smell will come up again.

So, apart from not eating it, another remedy is in the cooking:

If you make the garlic boil before using it, the high temperature will inibite the production of the smelling agent, and you'll not have this killing smell.

References:

http://www.placidasignora.com/2011/01/14/chi-laglio-mangia-daglio-sa-rimedi-contro-il-puteolare/

http://benessere.atuttonet.it/consigli/rimedi/alito-aglio-rimedi.php